# Wouldn't the Earth appear curved, even if it were flat?

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Hello everyone, I'm a normal guy with an interest in science but no real knowledge of physics (think Bob Lazar) and I'm looking for people who are smarter than I am to answer questions I have about the universe and make me feel all warm inside. First off I would like to say I'm not a flat earther by any stretch, but one of the most common critiques of flat earth theory is that photos from high altitude clearly show a curvature of the Earth. According to general relativity however, wouldn't the Earth from far enough away appear curved even if it were flat, due to gravitational lensing?

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It’s a matter of how much curve, and the thing about physics is we quantify things. So the question becomes “how much curvature?” The amount of lensing from the sun was hard to measure. The lensing from the earth would not be visible to the naked eye.

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Is there an equation which is used to determine the amount of lensing? If the amount of lensing from something as massive as the sun is difficult to measure, I imagine that the gravitation's effect on light is there but quite small?

edit: NM I found this myself

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1 hour ago, swansont said:

It’s a matter of how much curve, and the thing about physics is we quantify things. So the question becomes “how much curvature?” The amount of lensing from the sun was hard to measure. The lensing from the earth would not be visible to the naked eye.

When you mention the "naked eye",  doesn't it seem curious that the tiny drop of "protoplasm" (I use the deplorably unscientific term loosely) in the lens of your eye, or the even smaller glass lens in your smartphone, can bend light sufficiently to produce sharp, detailed, distinct images.  Whereas the gigantically, vastly greater mass of planets, stars, and galaxies, with a "focal length" extending across the Universe for millions of light-years, can't bend light-rays enough to provide anything but a vague blurry image.

It seems a poor show to me.  Can't the Universe do better?  Could we improve its performance by designing "corrective" lenses to increase resolution?

Edited by Charles 3781

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Your eye bends light by refraction, the 'slowing' of light, as it passes from a less dense material to a more dense material, due to increased absorption/emission events.

Planets, stars and galaxies bend light gravitationally, and the Sun will bend light passing tangentially ( close ) to its surface, by only about 1.75 arcseconds.

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40 minutes ago, MigL said:

Your eye bends light by refraction, the 'slowing' of light, as it passes from a less dense material to a more dense material, due to increased absorption/emission events.

Planets, stars and galaxies bend light gravitationally, and the Sun will bend light passing tangentially ( close ) to its surface, by only about 1.75 arcseconds.

Thanks Mig for pointing out the distinction between refractive effects  and gravitational field effects - I'm very much obliged.to you!

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I'm really not a flat earther but...

If the air was replaced by some gas with a slightly higher density and refractivity, you would be able to shine a light beam round the world.

The air near the surface is denser than the air further up because of gravity.
The air is thin at the tops of mountains etc. There's no argument bout that.

And the refractive index rises with density.
So light traveling through air near the ground is slightly slower than light going through air higher up.

That means that a beam of light bends down slightly- it's a bit like a mirage

https://en.wikipedia.org/wiki/Mirage

In the right conditions, you could get the light beam to bend downwards at exactly the right rate to keep going round the world..

Edited by John Cuthber

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Wouldn't it be impossible for any object of sufficient mass to be technically 'flat', as it would curve space? Am I wrong here?

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Not sure if that is the way you meant it, but yes, a sufficiently massive body will bend space; and time also.
We call this bending of the combined space-time, gravity. Gravity tends to arrange things such that the most mass fits into the least space, and this is demonstrated by large masses tending to spherical, not flat.

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Really man, I'm not such an ignoramus that I don't know what gravity is 😆

My point though is that wouldn't those 'spherical' masses actually be FLAT masses in a curved, spherical space

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13 minutes ago, Jonah Thorsson said:

My point though is that wouldn't those 'spherical' masses actually be FLAT masses in a curved, spherical space

What makes you think that would be the case?

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Well in a way, wouldn't it be kinda hard to tell the difference?

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5 hours ago, Jonah Thorsson said:

Well in a way, wouldn't it be kinda hard to tell the difference?

The geometry of spacetime in and around a flat (presumably disk-like) distribution of energy-momentum is very different from the one of a spherical distribution - so the difference would be immediately obvious simply by considering the motion of other bodies (and light) in the vicinity.

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Are there any sufficiently massive disk-like objects in our known universe? The way I understand it, for an object to remain flat or disk-like it would have to be not very massive. Is that correct?

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On 9/3/2020 at 2:15 AM, Jonah Thorsson said:

According to general relativity however, wouldn't the Earth from far enough away appear curved even if it were flat, due to gravitational lensing?

The notion of curvature in Einstein's GR is intrinsic, so you would detect it by moving on it without aid from any external projection. You walk around trying to move as straight at possible and you get back to the same point? => It is curved.

You walk around along two different perpendicular paths in reverse order and you end up in different points? Example 10º north, then 10º east vs 10º east then 10º north. => different end points => It is curved.

Curvature is an intrinsic property.

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1 minute ago, joigus said:

The notion of curvature in Einstein's GR is intrinsic, so you would detect it by moving on it without aid from any external projection. You walk around trying to move as straight at possible and you get back to the same point? => It is curved.

You walk around along two different perpendicular paths in reverse order and you end up in different points? Example 10º north, then 10º east vs 10º east then 10º north. => different end points => It is curved.

Curvature is an intrinsic property.

Right, so wouldn't light moving in curved space appear curved even though it's travelling as straight as possible? Is light somehow immune to the effects of curved space due to it's having no mass?

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2 minutes ago, Jonah Thorsson said:

Right, so wouldn't light moving in curved space appear curved even though it's travelling as straight as possible? Is light somehow immune to the effects of curved space due to it's having no mass?

Those are very different scales of curvature we're talking about. One of them is controlled by c (the speed of light in vacuum) as compared to the gravitational potential, and c is a very high-value constant in human terms. The other is controlled by the average radius of the Earth (as compared to linear displacements on its surface), which is the order of thousand of Kms, so it's much easier to detect, really. That's why the curvature of the Earth was discovered many hundreds of years ago and the curvature of photon's trajectories came much much later.

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Light is affected by space-time curvature, and, as we use light to determine 'straightness', we can't tell that it bends.

The electromagnetically affected parts of galaxies are disc shaped.
The electromagnetically transparent parts ( dark matter ) are spherically distributed.

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8 hours ago, MigL said:

Light is affected by space-time curvature, and, as we use light to determine 'straightness', we can't tell that it bends.

This is an interesting point. Surely we can see that light is capable of bending,  by refracting a ray of light through a prism, or a lens. The same effect is visible when the Sun is setting. As the Sun gets close to the horizon,  it appears bent sideways into a squashed oval shape.  Also changing colour from white to orange or red.

These effects aren't due to any "spacetime" curvature.   Only to refraction of light through a denser medium than a vacuum. In the case of the prism/lens, the medium is glass. And In the case of the sunset, the medium is the Earth's atmosphere.

And isn't the entire Universe filled with a kind of "atmosphere"?  In the form of interplanetary, interstellar, and intergalactic gas.  Admittedly this gas may be very thin.  But it extends for billions of light-years across the Universe.  So it might produce refractive effects on light-beams travelling through it. Could that explain why the light from distant objects appears "red-shifted".  Not because of any accelerating  "expansion of space", or "space-time curvature".

But just an optical effect resulting from  the light's passage through gas?

Edited by Charles 3781

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26 minutes ago, Charles 3781 said:

This is an interesting point. Surely we can see that light is capable of bending,  by refracting a ray of light through a prism, or a lens. The same effect is visible when the Sun is setting. As the Sun gets close to the horizon,  it appears bent sideways into a squashed oval shape.  Also changing colour from white to orange or red.

These effects aren't due to any "spacetime" curvature.   Only to refraction of light through a denser medium than a vacuum. In the case of the prism/lens, the medium is glass. And In the case of the sunset, the medium is the Earth's atmosphere.

And isn't the entire Universe filled with a kind of "atmosphere"?  In the form of interplanetary, interstellar, and intergalactic gas.  Admittedly this gas may be very thin.  But it extends for billions of light-years across the Universe.  So it might produce refractive effects on light-beams travelling through it. Could that explain why the light from distant objects appears "red-shifted".  Not because of any accelerating  "expansion of space", or "space-time curvature".

But just an optical effect resulting from  the light's passage through gas?

The reddening we see with the setting Sun is due to the blue end of the spectrum being scattered.  Thus the light coming from the direction of the Sun has less Blue light and looks redder.

The red-shft we see from distant galaxies cannot be due to a like effect.  We measure red-shift by looking at the light's spectrum.  In it are patterns of lines that are like "fingerprints" for elements.  Each pattern isn't only unique, but it is produced in a certain point of the spectrum.   If the red-shift was due to a scattering out of blue light, all you would see would be a dimming in the blue end of the spectrum. The spectral lines would still be there and in the same place.

This is not what we see. Instead we see a shift of the whole spectrum towards the red.  Spectral lines have moved further to the red end of the spectrum. The wavelength of the light itself has been changed, rather than  just certain frequencies filtered out leaving redder light behind.  (in fact, red-shifting will shift non-visible frequency ultraviolet into the visible light range.)

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18 hours ago, Jonah Thorsson said:

Are there any sufficiently massive disk-like objects in our known universe? The way I understand it, for an object to remain flat or disk-like it would have to be not very massive. Is that correct?

Many (but not all) galaxies are approximately disk-shaped to varying degrees, so these would be good examples. Another example that comes to mind would the accretion disk around a large black hole.

18 hours ago, Jonah Thorsson said:

Right, so wouldn't light moving in curved space appear curved even though it's travelling as straight as possible?

Of course. Light must follow geodesics of spacetime, just like anything else that is in free fall (it doesn’t matter if they are massless or not). The most striking and obvious example of this would be gravitational lensing.

9 hours ago, Charles 3781 said:

But just an optical effect resulting from  the light's passage through gas?

No, because cosmological redshift isn’t the same as optical scattering or refraction, as Janus has pointed out above. More crucially, it is not the only phenomenon that would be hard to explain within a static universe. To put it simply, if we consider all available data (not just a single isolated phenomenon such as redshift), then the Lambda-CDM cosmology is by far the best model that can explain them in one coherent framework, which is also compatible with everything else we already know about physics.

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but what about galactic spin in that the stars at the edge of the galaxy are moving close to the same speed the star at the center are moving? shouldn't that be impossible with that model??

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3 minutes ago, lemniskate said:

but what about galactic spin in that the stars at the edge of the galaxy are moving close to the same speed the star at the center are moving? shouldn't that be impossible with that model??

This is a valid question in its own right, but it isn’t directly related to the topic of this discussion. It would be better to start a new thread on this.

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