0895: "Teaching Physics"

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Mental Mouse
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Re: 0895: "Teaching Physics"

Postby Mental Mouse » Wed May 11, 2011 1:12 am UTC

KeithIrwin wrote:It's not a simpler hypothesis. It's clearly more complex. But it's more accurate ...


When it comes to scientific theories, the preference is Simple < Accurate < Predictive < Fruitful. Predictive is when you can use it to predict previously-unseen phenomena, and Fruitful is when you can make gadgets out of it, and/or use it to learn new things.

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Robot_Raptor
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Re: 0895: "Teaching Physics"

Postby Robot_Raptor » Wed May 11, 2011 3:20 pm UTC

Mental Mouse wrote:...Simple < Accurate < Predictive < Fruitful...


Wait, is 'Fruitful' part of the equation at all? As I understood it, scientists want more predictive science that helps us understand our universe better. That we get nice things like computers and space travel out of it is simply a fringe benefit. Useful to the layman ... well everyone really, but is it more important to science than predictiveness?

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Wed May 11, 2011 4:28 pm UTC

Robot_Raptor wrote:
Mental Mouse wrote:...Simple < Accurate < Predictive < Fruitful...


Wait, is 'Fruitful' part of the equation at all? As I understood it, scientists want more predictive science that helps us understand our universe better. That we get nice things like computers and space travel out of it is simply a fringe benefit. Useful to the layman ... well everyone really, but is it more important to science than predictiveness?


I think the idea is that if you can use a theory to build something that couldn't be built according to older theories, that really shows your theory gives a better understanding of the universe. Like a "field testing". It's one thing to pass the written test, it's something else entirely to put your knowledge into practice.
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Karisma
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Re: 0895: "Teaching Physics"

Postby Karisma » Wed May 11, 2011 6:25 pm UTC

Most, if not all, of the things have been mentioned earlier (my registration mail got caught in the spam filter...) but if you feel like you want/need more explanation I'd recommend taking a look at www.relativitet.se (don't worry about the .se tag, it's all in English and there's pictures and MATLAB files too :wink: ).

That guy held the best lectures I ever attended and he named his PhD-thesis "Gravity Illustrated. Spacetime Edition" ^^

Apparently [url] is switched off, sorry for maybe making you have to copy/paste.

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Re: 0895: "Teaching Physics"

Postby Gamer_2k4 » Fri May 13, 2011 6:14 pm UTC

You people are all idiots, Randall included. There doesn't need to be any gravity in the model at all for the metaphor to work. Take a rubber sheet and push it down over the top of a sphere. Do you see how it STILL DEFORMS, even though there's NO ANTI-GRAVITY PULLING THE SPHERE UP? The sphere does NOT HAVE TO BE ACCELERATING in order for it to deform the sheet! It just needs to be present!

I mean, seriously, there are two and a half pages of self-proclaimed nerds babbling on about relativity and thinking they're smart because of it, and NO ONE can figure this out. You're all idiots.

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Re: 0895: "Teaching Physics"

Postby philip1201 » Mon May 16, 2011 8:57 pm UTC

Gamer_2k4 wrote:You people are all idiots, Randall included. There doesn't need to be any gravity in the model at all for the metaphor to work. Take a rubber sheet and push it down over the top of a sphere. Do you see how it STILL DEFORMS, even though there's NO ANTI-GRAVITY PULLING THE SPHERE UP? The sphere does NOT HAVE TO BE ACCELERATING in order for it to deform the sheet! It just needs to be present!

I mean, seriously, there are two and a half pages of self-proclaimed nerds babbling on about relativity and thinking they're smart because of it, and NO ONE can figure this out. You're all idiots.

What determines how hard you push down? The analogy works with gravity because objects are pulled down harder depending on their mass. With your analogy, it depends on an unknown and arbitrary outside force (your hand).

Also please read my previous post, since it explains why using gravity doesn't ruin the metaphor - the gravity in the metaphor is uniform in strength, a strength correlated to the flexibility of the material by the Gravitational constant, just like Newtonian gravity in a laboratory setting.

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Re: 0895: "Teaching Physics"

Postby RebeccaRGB » Mon May 16, 2011 9:17 pm UTC

I still think having two sheets, one above the object and one below, is the best way to make the metaphor work. So you don't need (any kind of) gravity to explain gravity. Of course the last physics class I had was 4 years ago; does anybody see a potential problem with that version?
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Re: 0895: "Teaching Physics"

Postby bigjeff5 » Mon May 16, 2011 10:27 pm UTC

The problem with the rubber sheet analogy is not actually a problem with the analogy at all, but how it is applied.

If you are placing a heavy ball on the sheet, and then placing a lighter ball on the sheet and allowing it to fall toward the initial object, you are doing it wrong. That's not how gravity works at all, the outside force of gravity is pulling on the smaller ball, drawing it toward the larger ball. In other words, it's gravity doing the work on your analogy, not the curvature of the sheet, which is what you are trying to (completely unsuccessfully) explain.

Placing the sheet on top of the ball instead of underneath it is not ideal either, because now your analog depends on the size of the object, instead of the mass of the object. With that analogy a large foam ball that weighs half an ounce is going to distort the sheet much much more than a half-ounce lead weight, which is not analogous to reality at all. Placing the objects on top will cause them to distort the sheet in almost exactly the same way (the denser object will come to a sharper point, which also happens to be exactly the way space-time behaves).

In the correct application of the analogy, you simply take a flat rubber sheet and draw a single straight line across it. Then you place a heavy object on the sheet and observe how the line curves, drawing it closer to the heavy object. The closer the line is to the object, the more it curves. This is how space-time works. The line itself is still moving straight relative to the rubber sheet, but the sheet itself is distorted, drawing the line toward the heavy object. An analog of multiple objects will work as well by making a grid, but you must glue the objects to the sheet to ensure gravity's pull on the objects is only creating the distortion, and not drawing the objects together on its own.

It's a tricky analogy, and used incorrectly can really confuse people. The key is that all things travel in a straight line through space-time, but mass distorts space-time. Objects travel through the sheet, not on top of it. Another way of looking at it is that gravity doesn't "pull" objects at all, it only pulls space-time, and objects just happen to collide and stick to each other because space-time has been twisted enough to not allow them to pass by each other. Even in their (apparently) curved arcs toward each other, relative to space-time they are on completely straight trajectories that happen to intersect thanks to the curvature of space-time.

Edited to clean it up a bit.

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Re: 0895: "Teaching Physics"

Postby bigjeff5 » Mon May 16, 2011 11:39 pm UTC

Jeff S wrote:I've seen that space-time warp explanation of gravity, and I *still don't understand it*. Ok, so gravity warps space time. That still doesn't explain how that translates into a force causing an acceleration on mass? Also, if it deforms space and time equally or proportionally, how would that be any different than spacetime not being deformed at all?



That's actually exactly what happens, but it all depends on your perspective to notice it. Take the GPS and the relativistic affects upon their clocks. GPS satellites are further from earth's gravity, and therefore their time is less distorted by it. With the bending of space-time, more mass = slower time, so the clocks on earth should be slower than the same clocks in space. However, special relativity states that the faster an object travels, the slower time moves from its perspective. Satellites have to move darned fast to stay in orbit, so this effect should also be noticeable, and the satellite's clock should be slower than its twin on the earth. Both of these effects are observed with GPS satellites. Because the earth is not spherical, but bulges at the equator, satellites at the equator must travel much faster to maintain a geosynchronous orbit than satellites at higher or lower latitudes. The net effect is that for geosynchronous satellites at the equator, the speed of the satellite cancels out the lower gravity, and the clocks don't need any adjusting. The effect cancels perfectly, because the speed of the earth's spin determines its shape, and therefore the distribution of mass and the distance any geosynchronous satellite will need to be in order to maintain orbit. For satellites at higher or lower latitudes must move slower to maintain a geosynchronous orbit, and therefore must orbit much further away from the earth, where gravity's effect is weaker. For these satellites, the speed is not enough to counter the lower gravity, which means the clocks in the satellites run faster than those on the ground and must be constantly updated.

As for where the force of gravity comes from, well, that's why we're spending hundreds of billions of dollars to build giant machines that smash sub-atomic particles at each other in order to find it. Nobody knows where the force of gravity comes from. There are some theories that have promise, like the existence of a graviton, but nobody actually knows. Even Einstein couldn't tell you what gravity was, he simply came up with an absolutely brilliant way to describe it with incredible (thus far perfect) accuracy. That still doesn't mean anybody knows what it actually is.

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Re: 0895: "Teaching Physics"

Postby ramparts » Wed May 18, 2011 12:23 am UTC

Pxtl wrote:Good to know I'm not the only one who hates the "rubber sheet" explanation - explaining gravity *with* gravity is circular reasoning. I've always thought that Gravitons provide the best understanding of gravity... although they don't really cover the spacetime-warping aspect.


Sorry, don't mean to be mean, but this made me chuckle.

"I've always thought that gravitons provide the best understanding of gravity... although they don't really cover the whole gravity aspect."

Gravity is the warping of spacetime. Use anything else (like as-yet-unobserved gravitons) and you're missing the point.

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Re: 0895: "Teaching Physics"

Postby collegestudent22 » Wed May 18, 2011 3:19 am UTC

bigjeff5 wrote:Even Einstein couldn't tell you what gravity was, he simply came up with an absolutely brilliant way to describe it with incredible (thus far perfect) accuracy. That still doesn't mean anybody knows what it actually is.


According to Riemann's metric tensor formulation, the warping of space-time is what causes the four fundamental forces - one of which is gravity. Given that Einstein's theory uses the metric tensor, it is faulty to say that it describes anymore than a warping of space that would result in the "force" of gravity. Other formulations also define the other forces (such as electromagnetism) as warping of space-time in different ways. Looking at it that way, the question is not what gravity is, but what causes space-time to warp in the first place?
Last edited by collegestudent22 on Wed May 18, 2011 8:08 am UTC, edited 1 time in total.

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Re: 0895: "Teaching Physics"

Postby dr pepper » Wed May 18, 2011 6:33 am UTC

collegestudent22 wrote:
bigjeff5 wrote:Even Einstein couldn't tell you what gravity was, he simply came up with an absolutely brilliant way to describe it with incredible (thus far perfect) accuracy. That still doesn't mean anybody knows what it actually is.


According to Riemann's metric tensor formulation, the warping of space-time is what causes the four fundamental forces - one of which is gravity. Given that Einstein's theory uses the metric tensor, it is faulty to say that it describes anymore than a warping of space that would result in the "force" of gravity. Other formulations also define the other forces (such as electromagnetism as warping of space-time in different ways. Looking at it that way, the question is not what gravity is, but what causes space-time to warp in the first place?


The flow of ether over areas of a varying phlogeston density. This can be observed in a sealed tank of ultra pure polywater at the bottom of a mineshaft.

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Re: 0895: "Teaching Physics"

Postby K^2 » Wed May 18, 2011 11:43 am UTC

ianfort wrote:Maybe the universe is on the surface of a rotating hypersphere, and massive objects pull the fabric outward because of the the centripetal force...

That... is... brilliant. Not the rotating hypersphere. That part's rubbish. But the idea that the distortions in space-time are due to energy trying to propagate along a "straight line" in some higher dimension while being constrained to our space-time manifold might actually be workable. It would explain perfectly why gravitational and inertial masses are equivalent. Though, I'm having hard time picturing something that would work with general solutions.

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Re: 0895: "Teaching Physics"

Postby collegestudent22 » Wed May 18, 2011 11:50 am UTC

K^2 wrote:But the idea that the distortions in space-time are due to energy trying to propagate along a "straight line" in some higher dimension while being constrained to our space-time manifold might actually be workable. It would explain perfectly why gravitational and inertial masses are equivalent. Though, I'm having hard time picturing something that would work with general solutions.


I don't know if that fits with the model of string theory (which seems to simplify to the equations that we know work to describe the forces). Maybe it does, though, given that we don't actually have a physical basis for string theory on the fundamental level.

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Re: 0895: "Teaching Physics"

Postby K^2 » Wed May 18, 2011 12:26 pm UTC

I don't know enough string theory to say if this is in any kind of disagreement. But seeing how there is still no serious experimental support for string theory, it really wouldn't be a deal-breaker. If it can be made to work as a classic field theory, I'd be happy with it.

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Re: 0895: "Teaching Physics"

Postby collegestudent22 » Wed May 18, 2011 12:36 pm UTC

K^2 wrote:But seeing how there is still no serious experimental support for string theory, it really wouldn't be a deal-breaker.


True, but it could contradict string theory, and it is so mathematically beautiful! But, yeah, the basic structure on this level is still pretty much impossible to test at this point in time. It could work. Maybe someone will attempt to put together a theory of it. I'm not sure a classic field theory would work, though, as it seems to have a different mathematical structure - at least on a cursory level.

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Wed May 18, 2011 4:37 pm UTC

K^2 wrote:It would explain perfectly why gravitational and inertial masses are equivalent.

Mach (via Einstein) already explained why that is so. It baffles me that people think this is still a mystery.
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Re: 0895: "Teaching Physics"

Postby K^2 » Wed May 18, 2011 7:06 pm UTC

And the fact that General Relativity actually disagrees with Mach's Principle does not bother you one bit, right? According to Mach's Principle, acceleration is relative. According to GR, acceleration is absolute.

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Wed May 18, 2011 7:33 pm UTC

K^2 wrote:And the fact that General Relativity actually disagrees with Mach's Principle does not bother you one bit, right? According to Mach's Principle, acceleration is relative. According to GR, acceleration is absolute.

Source for that please?
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Re: 0895: "Teaching Physics"

Postby K^2 » Wed May 18, 2011 9:13 pm UTC

Pfhorrest wrote:Source for that please?

Acceleration in GR is a covariant derivative, which is independent of frame of reference. Acceleration is absolute, and so you can measure acceleration of your own frame of reference absolutely. That's in any GR textbook. I hope I don't need to quote a specific one.

Mach's Principle leads to acceleration as relative quantity. If all masses accelerate at the same rate as your frame of reference, you cannot measure acceleration of your own frame of reference. This just follows from the principle itself.

These two statements are in contradiction. Is that sufficient, or do you need me to find someone else on internet who have claimed so?

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Re: 0895: "Teaching Physics"

Postby webgiant » Wed May 18, 2011 9:51 pm UTC

Chrisfs wrote:
SciBoy wrote:
KeithIrwin wrote:I had this same objection because the rubber sheet explanation is usually used to explain gravity, but the example itself depends on understanding gravity.

Actually, it doesn't. You don't need to understand gravity to know that a ball placed on a rubber sheet will pull the sheet down. That you can observe in reality without knowing anything about gravity at all. In this case this effect is used to explain how gravity affects space/time, not what gravity is. We still don't really know what gravity is, unless I missed some recent revelation, we don't know how gravity can affect stuff so far away.

Have they found the graviton?


It's under the couch. It's what causes other dropped objects to be drawn under the couch.

This explains why my oldest cat--who ate her vegetables as a young kitten (true story) and now understands that a mirror is not an alternate reality and understands the concept of 2D images being used to represent 3D objects--spends so much time behind and under the couch: she's using gravitons to refine her transporter device.

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Wed May 18, 2011 11:34 pm UTC

K^2 wrote:
Pfhorrest wrote:Source for that please?

Acceleration in GR is a covariant derivative, which is independent of frame of reference. Acceleration is absolute, and so you can measure acceleration of your own frame of reference absolutely. That's in any GR textbook. I hope I don't need to quote a specific one.

Mach's Principle leads to acceleration as relative quantity. If all masses accelerate at the same rate as your frame of reference, you cannot measure acceleration of your own frame of reference. This just follows from the principle itself.

These two statements are in contradiction. Is that sufficient, or do you need me to find someone else on internet who have claimed so?

Ok, now take frame dragging into account. Lets say, magically somehow like in your description above, all the masses in the observable universe began moving, all along the same vector, except for a spaceship that you are in. Your reference frame would be dragged along with them, and you would feel a "force" pressing you against the wall of your ship in the direction that the rest of the universe was moving, yes? How would you be able to discern that state of affairs from your ship (somehow, magically) being moved in the opposite vector? Aside from even observable means of discerning, how would the mathematical descriptions of those two scenarios differ? Against what frame of reference are you differentiating the universe moving relative to your ship, versus your ship moving relative to the rest of the universe?

A acceleration just is a change in your reference frame. That may be a covariant derivative: you can always tell when your reference frame is changing, i.e. when you are accelerating, without needing to make reference to other objects to describe how it is changing. But that doesn't change the fact that your reference frame can be affected (and changed) by the motion of other massive objects.
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Re: 0895: "Teaching Physics"

Postby K^2 » Wed May 18, 2011 11:53 pm UTC

Two problems with the above. First of all, frame dragging causes acceleration of a reference frame. Agreed, you might call that semantics, but it is technically important for the next point. Suppose, the universe consists of you and a billion ton object. That object accelerates, and you feel the tug. Now suppose, the universe consists of you and a two billion ton object that accelerates at the same rate. In GR, the frame drag will be different. According to Mach's Principle, it will be the same. No other reference objects, so you'll experience acceleration equal to acceleration of reference object regardless of later object's mass. While the two theories predict the same qualitative effect, quantitatively, they are not in agreement.

The underlying theory might still agree with Mach's Principle. If you get effects like gravitational constant being function of universe's total energy, then the frame drag might end up being exactly the same in the above two examples. But in General Relativity the speed of light and gravitational constant are fixed. The acceleration will be a function of object's mass, and you are still left with a contradiction.

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Thu May 19, 2011 12:14 am UTC

K^2 wrote:Two problems with the above. First of all, frame dragging causes acceleration of a reference frame. Agreed, you might call that semantics, but it is technically important for the next point. Suppose, the universe consists of you and a billion ton object. That object accelerates, and you feel the tug. Now suppose, the universe consists of you and a two billion ton object that accelerates at the same rate.


At the same rate as you? I.e. you and the billion ton object accelerate together, and remain comoving? (Just trying to follow your description accurately).

In GR, the frame drag will be different. According to Mach's Principle, it will be the same. No other reference objects, so you'll experience acceleration equal to acceleration of reference object regardless of later object's mass. While the two theories predict the same qualitative effect, quantitatively, they are not in agreement.


Since I'm not clear on your description above, I may be misunderstanding you, but it seems to me that if you and the billion ton object are accelerating so as to remain comoving, then in GR you would feel the pull of the moving billion ton object along one vector, and you would feel the push of your own acceleration along another vector, and the two would cancel out, leaving you feeling exactly the same forces as you did before you and the billion ton object accelerated, exactly as Mach's principle would predict (since by Mach's principle neither of you would have "really" accelerated).

Say you were inside an impossibly sealed box through which no observations can be made, completely opaque to all electromagnetic radiation, a perfect thermal and electrical insulator, chemically inert, of infinite tensile strength, etc -- a GP Hull from Known Space, if you will, but without the transparency to visible light. You are sitting in the dark in this box in freefall in open space, and then you feel a "force" like acceleration. You can infer from the vector of this force that the ship is moving in a certain fashion, and assuming that the rest of the objects in the universe are static relative to each other and your previous reference frame, you could infer in what fashion you would see the rest of the universe whizzing past you, if you could see outside the ship.

But frame dragging, caused by objects whizzing under their own power past you in a stationary ship, could cause similar measurements from inside your ship. My question is, would your inferences of what you would see outside your ship (if you could) be any different if you assumed the forces you felt were cause by frame dragging, versus being caused by your ship accelerating under it own power?

E.g. say the universe consists of a billion ton hollow sphere with your spaceship in the center of it, and the inside of the sphere is marked with degree marks. If the sphere were to spin around your ship, then due to frame dragging you would feel dizzy. If your ship were to spin inside the sphere, then you would also feel dizzy. If you could see outside your ship, you would see the degree marks passing by as you, or the sphere, spun. Given that you can't see outside your ship, and you don't know whether you're spinning or the sphere is spinning, would your prediction of how fast the degree marks would pass you by differ between the assumption that you are spinning and the assumption that the sphere is spinning?

And if your ship, or the sphere, spun up in turn to keep up with the other, wouldn't you feel nothing (and predict, accurately, that you would see no degree marks flying past) in either case?

The underlying theory might still agree with Mach's Principle. If you get effects like gravitational constant being function of universe's total energy, then the frame drag might end up being exactly the same in the above two examples. But in General Relativity the speed of light and gravitational constant are fixed. The acceleration will be a function of object's mass, and you are still left with a contradiction.

I admit I am not so well versed in the math here; can you tell me, is the gravitational constant fixed by GR because of any mathematical necessity (i.e. could we compute a priori what the gravitational constant has to be), or is it just an observed value that we plug into the equations to make the units come out right? I was under the impression that it was the latter, in which case nothing is broken by the value of that constant being a function of the universe's total energy; we would just have an explanation for why the constant is such.

It occurs to me now that your answer to the above scenario of the billion-ton sphere and the perfectly opaque ship probably depends heavily (no pun intended) on the mass of the sphere; a lighter or heavier sphere would give different degrees of discrepancy from what you'd expect from Mach's principle, given our current value for the gravitational constant, which will be used to calculate how much the spinning sphere drags your frame. In that case, then we should be able to infer from Mach's principle and the observed value of the gravitational constant what the mass of the universe is. That gives us an empirical test for Mach's principle: what is the mass M which such a hollow sphere would have to have, for the frame-dragging effects of it spinning (as calculated with the observed value of gravitational constant) to equal the acceleration experienced by a ship spinning at the same speed in open space (as calculated with the same gravitational constant value)? Mach's principle predicts that that the mass of the universe should then be M. What is the mass of the universe as observed by other means, and how well does it match M?

It would make sense that we should be able to measure the mass of the universe from some local phenomenon, anyway, given that every mass in the universe affects every other mass. We should be able to pick a local mass, and measure how much it is being affected by the mass of the rest of the universe, and from that calculate what the mass of the rest of the universe is, no?

Addendum: Really going out on a limb here now, but follow this. Given Mach's principle, the gravitational constant is proportional to the mass of the observable universe, as above. The rate of the universe's expansion is (uncontroversially) inversely proportional to the gravitational constant, i.e. higher constant would mean slower expansion, lower constant would mean faster expansion. In an expanding universe, more and more distant mass is constantly leaving the cosmic event horizon, i.e. becoming unobservably distant, as more distant objects appear to be moving away from us proportionally faster and so sufficiently distant objects appear to recede faster than light and vanish from observability. Since the effects of gravity also propagate at c, the gravitational effects of such objects beyond the cosmic event horizon should also be lost... decreasing the mass of the observable universe, which per Mach's principle should decrease the gravitational constant, in turn accelerating the expansion of the universe.

Mach's principle explains the accelerating expansion of the universe!

EDIT: Expansion. (No pun intended).
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Re: 0895: "Teaching Physics"

Postby K^2 » Thu May 19, 2011 10:04 am UTC

No co-acceleration. Forget that. You are making things more complicated than they need to be. Mach's Principle first. A massive object accelerates relative to you. Since it is the only object in the universe of significant mass, its acceleration relative to you is what you are going to measure by an accelerometer you keep with you, because there is no other reference. Acceleration relative to massive object must be your true acceleration. Double the mass of that object, and nothing changes. Now GR. Massive object accelerates. Frame dragging causes some measurement on accelerometer. Double mass of the object, and you double the reading. Two entirely different predictions for the same setup.

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Re: 0895: "Teaching Physics"

Postby collegestudent22 » Thu May 19, 2011 11:40 am UTC

Basically, Mach's Principle is not compatible with GR's equivalence principle?

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Thu May 19, 2011 4:28 pm UTC

K^2 wrote:No co-acceleration. Forget that. You are making things more complicated than they need to be. Mach's Principle first. A massive object accelerates relative to you. Since it is the only object in the universe of significant mass, its acceleration relative to you is what you are going to measure by an accelerometer you keep with you, because there is no other reference. Acceleration relative to massive object must be your true acceleration. Double the mass of that object, and nothing changes. Now GR. Massive object accelerates. Frame dragging causes some measurement on accelerometer. Double mass of the object, and you double the reading. Two entirely different predictions for the same setup.

How does it contradict Mach's principle that your inertia would be relative to the mass of other objects in the universe, and thus the acceleration you measure will be doubled by a doubling of the only other mass in the universe, as GR predicts via frame dragging? That sounds right in the same vein. I'm proposing that frame dragging is a consequence or application of Mach's principle (Wikipedia agrees, in the article I linked earlier), that inertia is due to frame dragging (so you will measure different acceleration from the same motion depending on the mass of the rest of the universe; "frame dragging" as we think of it is just the effects of local masses on your inertia overwhelming the effects of the rest of the universe on it), and that it should thus be no surprise that inertial mass equals gravitational mass.

Same general line of thought I posed before can be posed in your scenario: an incredibly massive shell of matter of immeasurably large diameter is the only other object in the universe, and you are somewhere in the middle of it. Under Mach's principle, its acceleration relative to you is what you are going to measure by an accelerometer you keep with you, since it is the only other object in the universe. What is that measurement? Now instead, accelerate yourself along the opposite vector, and measure again; by Mach's principle, those two measurements should be the same, regardless of the mass of the shell; Mach's principle doesn't dictate that the mass of the shell has no effect, it only dictates that you measure the same acceleration regardless of whether the shell moves or you move, since they are by that principle equivalent scenarios.

Under GR, using our measured value of the gravitational constant, the difference in predicted measurements of you moving vs the shell moving will vary based on the mass of the shell (the you-moving measurement will not vary, but the shell-moving measurement will). We could also twerk the difference, given a fixed mass of the shell, by adjusting the value of the gravitational constant in our calculations. Since Mach's principle says that difference should be zero, then given our observed gravitational constant, the mass of the shell necessary to make those two measurements equal should be the observed mass of the universe, so that if you somehow moved the universe, the frame-dragging thereof would apply an equivalent force as if you moved along an opposite vector in a still universe (since Mach's principle says those are the same scenario). Or more generally, Mach's principle says that the observed gravitational constant should be proportional to the observed mass of the universe such that that difference is zero, since there is no difference between you moving relative to a mass and that mass moving relative to you, without some further masses to refer to.
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Re: 0895: "Teaching Physics"

Postby K^2 » Thu May 19, 2011 10:12 pm UTC

Pfhorrest wrote:How does it contradict Mach's principle that your inertia would be relative to the mass of other objects in the universe, and thus the acceleration you measure will be doubled by a doubling of the only other mass in the universe, as GR predicts via frame dragging?

You seem to have trouble with relative accelerations. If entire universe accelerates relative to you at acceleration a, your acceleration relative to entire universe is -a. Doesn't matter what the mass of the universe is. If your acceleration relative to entire universe is -a, your accelerometer must measure exactly -a. That's Mach's Principle. If it measures ANYTHING other than -a, there is a preferred frame of reference.

Maybe it's simpler if you think about velocities instead. Imagine there was a device that measures speed of an object, and it works regardless of frame of reference. If you increase velocity by some v, then the measurement increases by that v. Suppose, someone proposed that it measures speed relative to the massive objects in the universe, and is therefore not a violation of relativity. (Lets say Galilean Relativity for simplicity of example.) Then you show that when that the object moves relative to all universe with velocity v, it doesn't measure v, but rather some fraction of v which depends on mass of the universe. Yet, it measures changes in v correctly. The only way that can work is if there is some other frame of reference from which velocity is measured, and it is further offset by "drag" from massive objects. But that drag doesn't even matter now. You have an absolute frame of reference velocity relative to which you can objectively measure. That's a violation of relativity.

Just the same, if you can measure acceleration, and it comes out as anything other than acceleration relative to the whole of the universe, Mach's Principle is violated. If frame dragging from whole universe would give you exactly the right acceleration every time, then yes, these would be two different explanations of the same thing. But in GR, that does not happen. Acceleration due to frame dragging depends on mass of the universe, and that's a violation.

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Thu May 19, 2011 11:56 pm UTC

K^2 wrote:You seem to have trouble with relative accelerations. If entire universe accelerates relative to you at acceleration a, your acceleration relative to entire universe is -a. Doesn't matter what the mass of the universe is. If your acceleration relative to entire universe is -a, your accelerometer must measure exactly -a. That's Mach's Principle. If it measures ANYTHING other than -a, there is a preferred frame of reference.

By "the acceleration you measure", I am talking about what an accelerometer would show; not what you would compute by taking repeated distance measurements between you another object and plotting that curve or some such. That was the point of the opaque ship. You can't see outside to measure your "true" acceleration, but you have a device inside the ship which can measure acceleration via the effects of inertia.

According to Mach's principle, if you are in this ship and accelerate at A (as measured in m/s^2), your accelerometer will measure A (in Newtons of force divided by a known mass in the accelerometer). And if the universe somehow accelerates at -A (as measured in m/s^2), your accelerometer will also measure A (in Newtons of force divided by a known mass in the accelerometer), because according to Mach's principle those two situations are actually the same situation.

According to GR, if you are in this ship and accelerate at A (as measured in m/s^2), your accelerometer will measure A (in Newtons of force divided by a known mass in the accelerometer). And if the universe somehow accelerates at -A (as measured in m/s^2), your accelerometer will measure something (in Newtons of force divided by a known mass in the accelerometer) due to frame dragging, the value depending on the mass of the universe.

If Mach's principle and GR are both true, then the mass of the universe must be such that your accelerometer would read A (in N/kg) due to frame dragging when the universe accelerates at -A; and conversely, that if the mass of the universe was somehow cut in half, and then you accelerated your ship by A (in m/s^2), your accelerometer would measure 0.5A (in N/kg) (and it would take half as much thrust force to attain that acceleration). We can't test the latter because we can't suddenly cut the mass of the universe in half, but we could test the former by measuring the mass of the universe by other means and seeing how close it comes to the figure GR+MP would predict.

The explanation for why the latter would be so, why accelerometers would become inaccurate if the mass of the universe changed, is that the force which the test mass in your accelerometer is experiencing, the inertia which is holding it in your initial frame of reference against the changing motion of your ship, the force which the accelerometer measures and divides by the known measure of that mass to give you a figure in m/s^2... is the gravity of the rest of the universe, dragging said mass's reference frame with it. Gravity which of course varies by the mass of the rest of the universe. Which is how, getting back to my initial point, Mach's principle explains why inertial mass equals gravitational mass: inertia is caused by gravity.

I'm surprised you're so resistant to the compatibility of Mach's principle and GR. Einstein himself, the creator of GR, was a proponent of Mach's principle, and coined the name of it; the relativity of all frames of reference which is central to Mach's principle is likewise what GR is in turn named after. You sound almost like you are arguing that you can use acceleration to prove there is a preferred frame of reference, in contrast to Mach's principle; but a preferred frame of reference is one of the first things that GR (even SR) rejects. Your initial counterpoint was that acceleration can be measured irrespective to the motion of any other objects, as by an accelerometer; but then you quickly accept that large masses moving around an accelerometer will affect its readings, however slightly, via frame dragging. Why is accepting that the measurements of all accelerometers are always being likewise affected by all the mass in the universe so much a bigger step?
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Re: 0895: "Teaching Physics"

Postby K^2 » Fri May 20, 2011 12:51 am UTC

According to GR, if you are in this ship and accelerate at A (as measured in m/s^2), your accelerometer will measure A (in Newtons of force divided by a known mass in the accelerometer). And if the universe somehow accelerates at -A (as measured in m/s^2), your accelerometer will measure something (in Newtons of force divided by a known mass in the accelerometer) due to frame dragging, the value depending on the mass of the universe.

And you really can't tell that this implies preferred frame of reference for acceleration? If acceleration A of the universe does not result in -A on accelerometer, acceleration is absolute.

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Re: 0895: "Teaching Physics"

Postby Pfhorrest » Fri May 20, 2011 5:50 am UTC

K^2 wrote:
According to GR, if you are in this ship and accelerate at A (as measured in m/s^2), your accelerometer will measure A (in Newtons of force divided by a known mass in the accelerometer). And if the universe somehow accelerates at -A (as measured in m/s^2), your accelerometer will measure something (in Newtons of force divided by a known mass in the accelerometer) due to frame dragging, the value depending on the mass of the universe.

And you really can't tell that this implies preferred frame of reference for acceleration? If acceleration A of the universe does not result in -A on accelerometer, acceleration is absolute.

Which is why, if Mach's principle and GR are both true, the mass of the universe must be such that if the universe accelerated by -A, the accelerometer would measure a force due to frame dragging equivalent to the force of inertia it would measure if the ship had accelerated by A. I'm not proclaiming that its mass is such; I'm saying that this would be an empirical test of Mach's principle.

An accelerometer does not measure acceleration directly. It does not somehow magically compare your position to a reference position in absolute space over time and compute the rate of the rate of change of that position, distance per time per time, which is what acceleration truly is. The accelerometer measures a force, which is not equal to acceleration alone, but to mass times acceleration, and then given known figures for the mass involved, it can back-calculate acceleration from that force. Why is it then surprising that when measuring the (given Mach's principle) equivalent motion of the rest of the universe in the opposite vector, that the mass of the rest of the universe is relevant to what force the accelerometer would measure?

Say we posit the ship is somehow held stationary relative to absolute space, whatever that is; that is, we grant for a fact that it is actually, truly not accelerating. There are some large masses around it, in the same reference frame, but they are positioned such that their gravitational attraction cancels out, the ship is still in free fall, and the accelerometer still reads 0. Then one of the masses begins to spin very, very rapidly; due to frame dragging, the accelerometer measures a force and gives a nonzero reading... but, gasp, the ship is actually not accelerating, because we have stipulated that it is somehow pinned in place relative to absolute space! The accelerometer is wrong, because it doesn't know anything about frame-dragging and assumes that any force it measures is due to its own motion.

We would even have this problem if we simply posited that the ship was somehow pinned to absolute space, and there was just a single large mass next to it, no frame dragging involved. The accelerometer would show that the ship is accelerating, and GR says that if the ship is not falling freely into the mass that is is in fact accelerating, but you posit that there is some kind of absolute space that it could nevertheless be stationary to and thus not truly accelerating; thus, the accelerometer does not actually measure acceleration directly, because it gives a nonzero reading in a scenario where zero acceleration is stipulated.

I'm still coming to grips with the fact that you're advocating an absolute, preferred frame of reference in defence of relativity. I didn't get that that's where you were arguing toward at first, but now that you make it clear I'm kind of boggling. If relativity has a single defining characteristic, it is precisely the absence of such a preferred frame of reference; so that you try to use one to argue for the other just doesn't make any sense at all.
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Re: 0895: "Teaching Physics"

Postby PeterJThomas » Fri Jun 17, 2011 8:19 pm UTC

My first post here (joining an internet BB - seems so 1998!):

I was inspired enough by "Teaching Physics" to parlay it into a blog article: Analogies (http://peterjamesthomas.com/2011/05/19/analogies/).

Anybody else spend their time writing around xkcd? If so, I'd be interested to read your work.

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Re: 0895: "Teaching Physics"

Postby Notme » Fri Apr 05, 2019 12:34 am UTC

So, what if this model is closer then expected? Only, there are two sheets held together, attempting to achieve a state of order. The deformation is equivalent in both sheets, and the force imparted could be similar, depending on the properties of the sheet.

The state of order would be achieved when the sheets are as close together as possible, assuming order refers to parallel.


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