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Is there a physicist in the house?


boriz

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I'm pretty poor with maths, and my understanding of General Relativity is basic, but I had this idea, and I'm wondering if it holds water.

Many people will have heard of the balloon with dots on it being inflated to illustrate expanding 4d space, redshift and why the universe has no 3d center.

Well space isn't just expanding. The expansion is accelerating. This means that there are no truly inertial reference frames in the universe. Everything is always accelerating, in 4d. Could this be the source of gravity? All mass distorts the fabric of spacetime as it resists this acceleration ?

I know it's more Issac than Albert, but to create my own rubber sheet analogy...

Imagine the ubiquitous rubber sheet inside the ubiquitous space ship without a window, and you are accelerating at 1g. No way to tell you're not standing still on earths surface right? Equivalence principle.

So you put a marble in the middle of your rubber sheet and it makes a small dimple, a 3d analogue of a 4d gravity well. It looks exactly like it would look here on earth. But now you tweak the engine to increase the acceleration to say 1.5g. What happens to the dimple? It gets deeper right? It would look like the marble has gained 'weight'. With the engine off, no matter how fast you are travelling, the marble will not distort the sheet, it has lost all of it's 'weight'. If you can picture this all shifted up one dimension, you'd say it had gained/lost mass.

My conjecture is that gravity is our 3d perception of the response of spacetime to mass being accelerated through 4d space. If expansion wasn't accelerating, there'd be no gravity. So, what do you think?

*Ducks for cover*

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On 11/10/2022 at 1:34 AM, boriz said:

My conjecture is that gravity is our 3d perception of the response of spacetime to mass being accelerated through 4d space. If expansion wasn't accelerating, there'd be no gravity. So, what do you think?

*Ducks for cover*

Really intriguing! I like this kind of conjecture.

One correction/caveat. The concept of a 3D expanding balloon is often used to illustrate the idea of metric expansion of 2-space, which can then be used to conceptually understand the metric expansion of 3-space. However, the expansion of 3-space itself is not occurring "in" 4-space. The universe is (as far as we can tell) topologically flat; it should not be supposed that the 3D universe is expanding in a 4-dimensional hypersphere.

So with that understanding: yeah, I can't think of any specific reason why the stress-energy momentum tensor that defines spacetime curvature in general relativity could not be the result of 4-dimensional acceleration. Whether true or not, it's certainly a great way to conceptualize it. However, if there is actul physical acceleration in 4 dimensions which causes gravity,, such 4-dimensional acceleration would be independent of the observable accelerating metric expansion of space. And we should be able to know this anyway because the rate of expansion of the universe has changed through its history, but there is no evidence that the degree to which mass curves space has ever changed through the universe's history.  

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57 minutes ago, sevenperforce said:

However, the expansion of 3-space itself is not occurring "in" 4-space. The universe is (as far as we can tell) topologically flat; it should not be supposed that the 3D universe is expanding in a 4-dimensional hypersphere.

IIRC the great Carl Sagan described it thus; Imagine you have an infinite source of sticking plasters, and you began making a ball with them. As the ball grows, the curve of the surface decreases until once the ball is half the size of the universe, the curve is zero (flat). Then if you continue, the curve becomes negative and you eventually find yourself in a confined spherical chamber, running out of space, with the rest of the universe solid sticking plasters.

I have often said, the only difference between the inside and the outside of a box is it's size, and that the angles of triangles add up to more than 180 degrees. Indeed, if the triangle was big enough, it's angles would all be 90 degrees.

A hypersphere is exactly how I picture it. Where did I go wrong?

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2 hours ago, boriz said:

A hypersphere is exactly how I picture it. Where did I go wrong?

Metric expansion can be conceptualized by imagining 1-space expanding around a 2D circle or 2-space expanding around a 3D sphere or 3-space expanding around a 4D hypersphere, but that doesn't mean the 4D hypersphere is the actual shape of the universe. It's just a concept to understand metric expansion without resorting to infinities.

I don't see any reason why gravity couldn't be the result of an acceleration in 4-space, but that acceleration, if it exists, is distinct from the metric expansion of the universe. 

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i guess its sort of like with quaternions where you simplify a 3d problem by making it a 4d problem. totally counter intuitive, and totally viable.

also been kind of curious about vsl theories. any observed curvature is just light diffracting as it changes velocities about gravity sources. i believe einstein considered this when coming up with gr.

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6 hours ago, Nuke said:

light diffracting as it changes velocities about gravity sources. i believe einstein considered this when coming up with gr.

Light follows the geodesic in distorted spacetime, making it appear to bend when it's actually following a straight line (shortest path). It doesn't spread the spectrum since it acts equally on all frequencies. Diffraction is an interference phenomena, spreading out the spectra as it passes an edge.

Did you ever fly a drone on a sunny day and notice that it's shadow had a bright halo? Or a similar effect when you look out of an aircraft window at it's shadow? That's diffraction.

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18 hours ago, sevenperforce said:

Metric expansion can be conceptualized by imagining 1-space expanding around a 2D circle or 2-space expanding around a 3D sphere or 3-space expanding around a 4D hypersphere, but that doesn't mean the 4D hypersphere is the actual shape of the universe. It's just a concept to understand metric expansion without resorting to infinities.

I don't see any reason why gravity couldn't be the result of an acceleration in 4-space, but that acceleration, if it exists, is distinct from the metric expansion of the universe. 

I'm a little concerned about viewing gravity as an expression of expansion.  

Also, am I correct that when Einstein framed his thought experiments (like the person in the elevator not being able to tell the difference between inside a box at rest on the surface of the planet from being inside one under constant acceleration in space) - he was making analogies.  I don't believe he was saying that experiencing gravity on the surface is exactly the same as being under constant acceleration.  While they may be for practical purposes relatively indistinguishable, they are functionally distinct.  (I accept that I'm being accelerated toward the center of the earth and resisted by its surface, which gives my mass weight, but I make the preceding statement/question because I don't think this next is true...)  

At least not to the point where you could say that infalling toward the center of the gravitational well of a planet and feeling your weight on your feet as the planet's surface resists your ability to infall further is the same thing as being at rest except for the expanding planet pushing against your feet creating the illusion of gravity.  That seems a step too far.

For gravity to be an expression of expansion the planet would have to be expanding in a way distinct from 'me' - I and the space I occupy could not be expanding similarly to feel the effect of the planet's expansion as gravity.  If everything in this local space were expanding uniformly, I would be expanding, the ruler I use to measure things would be expanding, etc. and so I would not experience gravity as an expression of expansion.  OTOH for gravity to be an expression of expansion me and my ruler would have to remain 'at rest' (or at least expand differently) from the planet, which would become measurably bigger all the time.

ja?

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16 hours ago, boriz said:

Light follows the geodesic in distorted spacetime, making it appear to bend when it's actually following a straight line (shortest path). It doesn't spread the spectrum since it acts equally on all frequencies. Diffraction is an interference phenomena, spreading out the spectra as it passes an edge.

Did you ever fly a drone on a sunny day and notice that it's shadow had a bright halo? Or a similar effect when you look out of an aircraft window at it's shadow? That's diffraction.

i may have use the wrong term there. maybe refraction, idk. i saw a few videos about it a few months ago and am trying to put it together from memory. maybe i should have just checked wikipedia

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5 hours ago, JoeSchmuckatelli said:

I'm a little concerned about viewing gravity as an expression of expansion. 

It certainly cannot be an expression of expansion within 3-space, which is why the ongoing and observable metric expansion of the universe is not the source of gravity.

5 hours ago, JoeSchmuckatelli said:

Also, am I correct that when Einstein framed his thought experiments (like the person in the elevator not being able to tell the difference between inside a box at rest on the surface of the planet from being inside one under constant acceleration in space) - he was making analogies.  I don't believe he was saying that experiencing gravity on the surface is exactly the same as being under constant acceleration.  While they may be for practical purposes relatively indistinguishable, they are functionally distinct.  (I accept that I'm being accelerated toward the center of the earth and resisted by its surface, which gives my mass weight, but I make the preceding statement/question because I don't think this next is true...)  

I could be wrong, but I don't believe they are in fact functionally distinct. They are the same. Special relativity says that it is 100% impossible to tell the difference between acceleration resulting from an external force and acceleration resulting from a gravitational field.

Now, a gravitational field will have tidal effects, which may be detected in some other way, but that raises issue of measuring the distances, which themselves are subject to the gravitational field, so special relativity holds.

5 hours ago, JoeSchmuckatelli said:

At least not to the point where you could say that infalling toward the center of the gravitational well of a planet and feeling your weight on your feet as the planet's surface resists your ability to infall further is the same thing as being at rest except for the expanding planet pushing against your feet creating the illusion of gravity.  That seems a step too far.

For gravity to be an expression of expansion the planet would have to be expanding in a way distinct from 'me' - I and the space I occupy could not be expanding similarly to feel the effect of the planet's expansion as gravity.  If everything in this local space were expanding uniformly, I would be expanding, the ruler I use to measure things would be expanding, etc. and so I would not experience gravity as an expression of expansion. 

You're correct that if 3-space was uniformly expanding at a certain rate (it's not uniform, even under metric expansion, until you get to intergalactic distances), then you wouldn't experience any acceleration. However, I don't believe that's quite what the OP is suggesting.

What OP is suggesting, as I understand it, is that there is a fourth spatial dimension which is undergoing some sort of acceleration, and it is the acceleration in that fourth spatial dimension which causes the stress-energy-momentum tensor to behave the way that Einstein's field equations say it behaves.

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1 hour ago, sevenperforce said:

What OP is suggesting, as I understand it, is that there is a fourth spatial dimension which is undergoing some sort of acceleration, and it is the acceleration in that fourth spatial dimension which causes the stress-energy-momentum tensor to behave the way that Einstein's field equations say it behaves.

Ah crap - now I have to google all those terms!

(which, tbh, is why I swim in these waters)

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On 11/13/2022 at 11:14 PM, sevenperforce said:

I don't see any reason why gravity couldn't be the result of an acceleration in 4-space, but that acceleration, if it exists, is distinct from the metric expansion of the universe. 

You're saying that, although the analogy works as a representation or model, reality could be more complicated/subtle and one should not be mistaken for the other?  I couldn't agree more, but doesn't that apply to all scientific theories?

Or did I misunderstand you? (Having not studied physics formally, I often find terminology is my biggest sticking point.)

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1 minute ago, boriz said:

You're saying that, although the analogy works as a representation or model, reality could be more complicated/subtle and one should not be mistaken for the other?  I couldn't agree more, but doesn't that apply to all scientific theories?

Or did I misunderstand you? (Having not studied physics formally, I often find terminology is my biggest sticking point.)

Your proposal that gravity could potentially be the result of 4-space acceleration has a chance of being not only useful for understanding, but actually true.

However, the comparison with the common analogy of metric expansion as the expansion of a 4D hypersphere is limited, because that is only useful for understanding and is not actually representative of reality as we know it.

Your conjecture may be correct. Maybe there really is an acceleration in 4-space causing the spacetime curvature we observe in 3-space. But even if that’s correct, that would be a separate acceleration/expansion/etc. than the metric expansion of the universe caused by dark energy. 

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LIGO works by measuring the time it takes for a LASER to travel between two distant points. It uses mirrors, many 'bounces', and interference to make it extremely precise. Am I correct?

Then it shouldn't work.

Gravity waves [GW] 'squeeze' spacetime, so any change in the distance between the mirrors is accompanied by a precisely equal change in the local 'rate of time'. The time it takes for the LASER to travel remains locally constant, even when squeezed by a GW. A shortening of the tunnel is accompanied by a slowing of local time and a proportional slowing of the local speed of light.

It's like you are using a ruler that changes length exactly in proportion to the thing you are measuring.

Huge candidate GW's should pass through the instrument and remain undetected.

What am I missing?

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8 hours ago, boriz said:

any change in the distance between the mirrors is accompanied by a precisely equal change in the local 'rate of time'.

This is the part that is wrong.

Time dilation does happen as a result of a gravitational field, but this effect is very small and requires an extremely strong gravitational field to even be measurable. For example, you are 1/6 as heavy on the moon as you are on Earth, but time does not pass 6 times faster on the moon. So it is not a “precisely equal change” at all.

The change in the rate of the passage of time associated by the small spacetime ripple that is a gravity wave is going to be incomprehensibly smaller than the ripple. 

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19 hours ago, darthgently said:

I can't keep up with all of this but it seems like it lends plausibility to the notion that our entire universe could be a spacecraft accelerating through 4D space to some destination.  Change my mind, ha

So you know this analogy, right?

teaching_physics.png

We know why objects have inertial mass: it's a combination of relativistic mass from bond energies and invariant mass from the Higgs mechanism. That all fits very nicely within special relativity. 

And we know that bent space changes the way that objects move. The basic description of general relativity is quite concise: Space-time tells matter how to move; matter tells space-time how to curve. An object in a gravitational field isn't actually being acted on by an outside force; rather, it's simply following a straight line in curved space. That's not THAT counter-intuitive.

What's a little more puzzling is WHY matter tells space-time how to curve. What is it about inertial mass which curves space? Why is it that space is always curved exactly the same amount for any specific amount of inertial mass? There's no apparent reason for this. You could imagine an object which has a lot of gravitational mass (curving space a lot) but little inertial mass, or an object which has a lot of inertial mass (high resistance to force) but very little gravitational mass, but that's never the case. Why not?

What the OP has conjectured -- and what doesn't seem to be entirely impossible, as far as I can tell -- is that perhaps the answer lies back in special relativity. Special relativity tells us many things, but one thing it assures us of is that there is no way to tell the difference between acceleration of your reference frame and acceleration due to gravity. If you are in a box and you measure your local g to be 3.721 m/s2, you could be on the surface of Mars. But you could also be in a spaceship accelerating at 3.721 m/s2, or you could be on an elevator on Earth accelerating downward at 6.09 m/s2, or you could be on the inner surface of a 744-meter-wide ring rotating at approximately 1 rpm. You don't know, and there's literally no way for you to find out.

Consider the rubber-sheet analogy above. The rubber sheet is a 2-dimensional analogue of 3-space. If a 2-dimensional sheet is placed in a gravitational field with a vector perpendicular to the plane, then mass will quite obviously stretch the 2-dimensional sheet into that third dimension, causing simulated gravity. But we also know that acceleration fields are source-invariant. So if you have a rubber sheet on a spaceship which is accelerating at 1 gee perpendicular to the plane of the sheet, then the same thing will happen.

All we have to do, then, is add another spatial dimension. If 3-space is being accelerated through 4-space, then the resistance of inertial mass to acceleration will cause the 3-space to curve into the 4th dimension, causing gravity.

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10 hours ago, sevenperforce said:

This is the part that is wrong.

Sorry, poor choice of words. Precisely proportional would be better.

The GPS network only works because the clocks compensate for the slowing of time here in earths gravity well. If you imagine a long wavelength GW passing through the earth, it would cause the whole planet to 'bob up and down', in 4space, alternately making the clocks slightly to fast, then slightly too slow. It would average out (like any AC signal), but the peaks and troughs would be perfectly synchronised to any measurable physical distortions, such as the measurements made at LIGO.

The magnitude of displacement that LIGO detects is less than the width of a proton, so even a tiny amount of time dilation could be sufficient to cancel it out. You can't separate space and time, it's one thing. Isn't it?

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7 minutes ago, boriz said:

Sorry, poor choice of words. Precisely proportional would be better.

{snip]

The magnitude of displacement that LIGO detects is less than the width of a proton, so even a tiny amount of time dilation could be sufficient to cancel it out. You can't separate space and time, it's one thing. Isn't it?

It's not proportional, though.

The displacement LIGO detects is indeed infinitesimal, but that means that its effect on time dilation is correspondingly that many billions of billions of trillions of times smaller.

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On 11/17/2022 at 11:49 PM, sevenperforce said:

It's not proportional, though.

Ok. That would explain it I suppose.

Thank you for indulging me. Next question:

Is 0.999r < 1?

If so, then 1/3 = 0.333r and 3*0.333r is 0.999r.

So 1/3*3 is <1?

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