0895: "Teaching Physics"

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Spectrum
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Re: 0895: "Teaching Physics"

Postby Spectrum » Fri May 06, 2011 2:56 pm UTC

The truth is a bit stranger than that. We humans have a hard time thinking without such analogies but all the evidence is that the reality *is* the mathematics. Physicists routinely construct pretty equations based on very noisy data, but better data shows the equations are accurate to many more decimal places than the data that went into constructing the equations. It is as if the laws of physics are somehow constrained to be simple equations.

This leads to the physicists' tendency to think of the equations as the Thoughts of God. As the shirt sold by the MIT Hillel says, "And God said '[Maxwell's equations]' and there was light." The Genesis version is an approximation due to limitations of Classical Hebrew for expressing vector calculus....

Nergye
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Re: 0895: "Teaching Physics"

Postby Nergye » Fri May 06, 2011 3:01 pm UTC

My take on this perceived problem with the rubber sheet analogy is as follows: First, it is a 2-dimensional model of a 3-dimensional system. That much is clear, but the problem people seem to have with it is that it ends up with the sheet distorted into a 3rd dimension, which doesn't seem to have a part in the analogy beyond that caused by how objects on the sheet react to it (eg, rolling down the slope, orbiting around a distortion of the sheet, etc.).

My solution to this is simply to look at the model from above - that way, it's still a 2-D model, and the objects still react in just the same way, but you don't have this seemingly meaningless extra dimension involved.

Sadly, this doesn't solve the problem of how to model the effects of large masses on the flow of time, but be fair. We're talking about a rubber sheet here. ;)

Blarg
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Re: 0895: "Teaching Physics"

Postby Blarg » Fri May 06, 2011 3:03 pm UTC

Don't you hate it when rubber sheets don't measure up to your needs?

bamapookie
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Re: 0895: "Teaching Physics"

Postby bamapookie » Fri May 06, 2011 3:08 pm UTC

Doesn't quantum physics teach us that you both are, and are not, Richard Feynman? I can't be sure. I've never observed you. (That may be an approximation, though.)

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SpringLoaded12
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Re: 0895: "Teaching Physics"

Postby SpringLoaded12 » Fri May 06, 2011 3:23 pm UTC

Wayfarer247 wrote:Of course, that guy reminds me of people I know who just love to analyze everything. It's a simile, get over it.

He strikes me as the type that overthinks jokes, or points out the flaws and holes in them. I hate that sort of thing.
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Nergye
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Re: 0895: "Teaching Physics"

Postby Nergye » Fri May 06, 2011 3:35 pm UTC

Blarg wrote:Don't you hate it when rubber sheets don't measure up to your needs?


Man, you have no idea how often I get that.

Jeff S
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Re: 0895: "Teaching Physics"

Postby Jeff S » Fri May 06, 2011 3:52 pm UTC

Ok, I'm going to chime in, because sometimes I'm "that guy". It's not because I'm a wiseguy or trying to cause trouble. It's that I'm trying to *understand*, and the problems in your analogy mean I don't actually understand the situation better than before the analogy.

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? Here's what I mean (and perhaps this arises from my fundamental misunderstanding): if you deformed space *without* any impact on time, we could tell we were going through a deformation because we could measure changes in our speed (distance covered per unit time) with no corresponding external force - which is a little bit like gravity. But, if space *and* time are being deformed, proportionally, then wouldn't your passage through space change at the same rate as your passage through time, and thus would end up appearing to be constant?

Also, we live in three-dimensional space. How is the deformation of a 2-dimensional plane analogous to deformation of 3-dimensional space? I can't map from 2D to 3D in this instance, at least not without some additional explanation.

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Samik
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Re: 0895: "Teaching Physics"

Postby Samik » Fri May 06, 2011 4:32 pm UTC

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

Oh, I thought it was under the front passenger's seat.

ianfort
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Re: 0895: "Teaching Physics"

Postby ianfort » Fri May 06, 2011 5:38 pm UTC

Doesn't the whole concept of wormholes only make sense if space is literally bending?

KansasBrad
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Re: 0895: "Teaching Physics"

Postby KansasBrad » Fri May 06, 2011 5:48 pm UTC

Space-time is like a rubber sheet -
and massive objects act like a significant other who tries to steal the covers and wrap them around themselves. :wink:

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ysth
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Re: 0895: "Teaching Physics"

Postby ysth » Fri May 06, 2011 6:10 pm UTC

Jeff S wrote:Ok, so gravity warps space time. That still doesn't explain how that translates into a force causing an acceleration on mass?


For that, you need to know what "force" really is, and how movement can ever change.
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SirMustapha
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Re: 0895: "Teaching Physics"

Postby SirMustapha » Fri May 06, 2011 6:51 pm UTC

SpringLoaded12 wrote:
Wayfarer247 wrote:Of course, that guy reminds me of people I know who just love to analyze everything. It's a simile, get over it.

He strikes me as the type that overthinks jokes, or points out the flaws and holes in them. I hate that sort of thing.


In other words: don't question the teacher. If you don't understand him, you're dumb.

Weird: when Randall points out that "deurr, if there are no falcons in the Star Wars universe, how can a ship be named the Millennium Falcon??", he's being a pedantic asshole but he's RIGHT; if a student points out a valid flaw in a scientific analogy, which potentially can harm the students' understanding of the concept in hand, he's being a pedantic asshole AND HE'S WRONG.

Роберт
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Re: 0895: "Teaching Physics"

Postby Роберт » Fri May 06, 2011 7:03 pm UTC

SirMustapha wrote:
SpringLoaded12 wrote:
Wayfarer247 wrote:Of course, that guy reminds me of people I know who just love to analyze everything. It's a simile, get over it.

He strikes me as the type that overthinks jokes, or points out the flaws and holes in them. I hate that sort of thing.


In other words: don't question the teacher. If you don't understand him, you're dumb.

Weird: when Randall points out that "deurr, if there are no falcons in the Star Wars universe, how can a ship be named the Millennium Falcon??", he's being a pedantic asshole but he's RIGHT; if a student points out a valid flaw in a scientific analogy, which potentially can harm the students' understanding of the concept in hand, he's being a pedantic asshole AND HE'S WRONG.

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arbivark
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Re: 0895: "Teaching Physics"

Postby arbivark » Fri May 06, 2011 7:53 pm UTC

Shaka, when the walls fell. Temba, his arms wide! Darmok and Jalad on the ocean.

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Re: 0895: "Teaching Physics"

Postby MSTK » Fri May 06, 2011 8:02 pm UTC

Jeff S wrote:Ok, I'm going to chime in, because sometimes I'm "that guy". It's not because I'm a wiseguy or trying to cause trouble. It's that I'm trying to *understand*, and the problems in your analogy mean I don't actually understand the situation better than before the analogy.

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? Here's what I mean (and perhaps this arises from my fundamental misunderstanding): if you deformed space *without* any impact on time, we could tell we were going through a deformation because we could measure changes in our speed (distance covered per unit time) with no corresponding external force - which is a little bit like gravity. But, if space *and* time are being deformed, proportionally, then wouldn't your passage through space change at the same rate as your passage through time, and thus would end up appearing to be constant?

Also, we live in three-dimensional space. How is the deformation of a 2-dimensional plane analogous to deformation of 3-dimensional space? I can't map from 2D to 3D in this instance, at least not without some additional explanation.


Hi.

Below is my explanation of General Relativity to someone with little physics experience, in an effort to answer your first question. It's a bit long however, so I'll spoil it out of courtesy.
Spoiler:
General relativity's explanation of gravity comes from a geometric and topological perspective.

Let's say you have a space in which points can exist. One fundamental thing you can do is define a "metric", which is a fancy word for "function to determine the distance between two points". In normal cartesian coordinates, your metric is a variation on the Pythagorean theorem -- no doubt you have learned the "distance formula" for 2D space. It's the square root of the sum of the squares of the differences in x and y. [imath]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/imath]

You can see that the "straight line" path of an object really is dependent on what really is a straight line according to this metric. In fact, because movement and distance are intertwined, you could say that an object's movement path depends largely on the metric at hand.

Consider now spaces where different metrics are used to measure distance. There are many classic examples in maths -- Hyperbolic Space, for example. And you can also see that even in spaces we encounter every day -- for example, a spherical space, our concept of distance must be re-assessed.

Perhaps we may even consider spaces with arbitrary metrics, for example -- a space in which the metric function [imath]d(x_1,x_2)[/imath] varies depending on the time of day, or something ridiculous, like...the presence of mass nearby the points.

General Relativity is at heart a metric. In GR, the "distance" between two points (in spacetime) is a function that takes into account the presence of masses in the space.

In these new spaces, you start seeing new "straight lines". You will see that a ball falling into a planet is not the planet pulling the ball into it, but rather the natural "straight-line path" of the ball.

Einstein's genius was creating a metric that aligned more or less exactly with what we observe from day to day.

Mass "deforms" spacetime in the sense that it "warps" the distances between points. Which really is a big part about what defines a space.


In your second question, I think you could probably answer it yourself if you thought about it.

Gravity deforms space and time, but you could tell if you are under gravitational influence regardless of how fast or slow you are going in time if you find out that you are no longer traveling in an apparent straight line.

For your third

The analogy shows that masses "distort" spacetime, as they change the distance metric and warp things a lot. You can sort of draw new "straight lines" and see that they sort of follow the curves created by the warping (sortaaaaaaaa).

In the same way if you imagined a 3D space, and place a mass in the middle, you can sort of imagine the mass "sinking into" the space and distorting/warping things around it. That's how you can sort of scale up the analogy.

Although in truth I feel like the main thing you gain from the rubber sheet analogy is that distortions in spacetime travel at a fixed speed that is related to the "viscosity" of the rubber sheet, as opposed to instantaneously as Newton implies.

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Re: 0895: "Teaching Physics"

Postby KrytenKoro » Fri May 06, 2011 8:05 pm UTC

I apologize if I'm mistaken, but isn't the rubber sheet analogy used to explain how gravity ALSO deforms space and time, and not to explain the cause of gravity?
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Retsam
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Re: 0895: "Teaching Physics"

Postby Retsam » Fri May 06, 2011 8:08 pm UTC

Spectrum wrote:This leads to the physicists' tendency to think of the equations as the Thoughts of God. As the shirt sold by the MIT Hillel says, "And God said '[Maxwell's equations]' and there was light." The Genesis version is an approximation due to limitations of Classical Hebrew for expressing vector calculus....

Moses: "Err... what?"

rcox1
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Re: 0895: "Teaching Physics"

Postby rcox1 » Fri May 06, 2011 9:03 pm UTC

Here is my take. Any valid model is approximate. It fixes variables as constants, it ignores higher order interactions, it focuses on a set of data that can efficiently computed, it makes assumptions that are defensible for the situation. The one dimensional motion of a ball being thrown up in the air, for example, can be written as x0+v0t+4.9t^2. This will allow us to predict, for example, how high the ball will go and how long it will be in the air given a certain newtonian reference frame and many other assumption. The model does not at all imply that there is no motion in the other two direction, that the ball is not a certain size of color. The equation does not even imply that what is being thrown is ball. What the equation does is a create a mathematical analogy, if you will, that model a certain aspects of kinematics. Other aspects exist, but in science, as in any endeavor where are trying to solve problems, we reduce the problem into simple steps, simply, and solve. In effect, we assume the spherical chicken, ignore all part that are not concerned with the problem at hand, and come up with a reasonable solution.

Like an equation, the rubber sheet analogy does not explain all of relativity, just part of it. It represents that we are no longer talking about fields, but geometry. It is an important distinction. I do not think the two dimensional nature of the sheet is not an issue. My understanding is that a three dimension universe can easily be created by integrating over the laminates. Likewise, the three model of local geometry tend to represented as two dimension surfaces.

What I like is that the cartoon is typical of a class. An relevant analogy is given in a effort to bridge past knowledge to current knowledge, and instead of trying to understand how the analogy functions, some students will find reasons to dismiss the analogy so as not to build understanding. Then, when the more mathematical explanation is give, the student will shut down. Science and math is hard. It makes everyone head hurt. That does not mean just give up.

And, just because, good luck to anyone taking the AP Physics exam monday afternoon. Y'all are the best.

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Re: 0895: "Teaching Physics"

Postby fredfnord » Fri May 06, 2011 9:27 pm UTC

As a someone who uses metaphors liberally just in my basic patterns of speech, I hate that one guy who always calls you out on the imperfections in every single one, as if you were trying to leverage each and every metaphor you've ever used to pull down the wool and slip some major fallacy past everyone for your nefarious purposes.


One of my science teachers had a solution for this. The first time someone nitpicked one of his metaphors, he said, 'Ah, yes, that's true. I can see you're paying attention. Was anyone else tempted to make the same observation?'

No one was.

'Very good. So, it looks like you're the only one with that species of brain damage. If you would prefer, I can raise my hand like this every time I'm about to use a metaphor, and you can put your fingers in your ears. That way we can get on with the teaching and you won't hear anything that offends you. Shall I?'

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Re: 0895: "Teaching Physics"

Postby colovelo » Fri May 06, 2011 9:31 pm UTC

arbivark wrote:Shaka, when the walls fell. Temba, his arms wide! Darmok and Jalad on the ocean.

Randall, his cheese burning!

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Re: 0895: "Teaching Physics"

Postby unus vox » Fri May 06, 2011 9:31 pm UTC

SirMustapha wrote:
SpringLoaded12 wrote:
Wayfarer247 wrote:Of course, that guy reminds me of people I know who just love to analyze everything. It's a simile, get over it.

He strikes me as the type that overthinks jokes, or points out the flaws and holes in them. I hate that sort of thing.


In other words: don't question the teacher. If you don't understand him, you're dumb.

Weird: when Randall points out that "deurr, if there are no falcons in the Star Wars universe, how can a ship be named the Millennium Falcon??", he's being a pedantic asshole but he's RIGHT; if a student points out a valid flaw in a scientific analogy, which potentially can harm the students' understanding of the concept in hand, he's being a pedantic asshole AND HE'S WRONG.


The best thing about you is how pedantic you get when Randall (who apparently is never tongue-in-cheek or self-acknowledging) appears to be hypocritical. It's like you've stumbled upon a conspiracy. Please go on. /popcorn
Spoiler:
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E_H
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Re: 0895: "Teaching Physics"

Postby E_H » Fri May 06, 2011 9:47 pm UTC

A better analogy than the rubber sheet, so accurate that it may not really be an analogy at all, is to regard the gravitational field as increasing the index of refraction of space. Where the gravitational field is high, the index of refraction is also high and light moves more slowly. Since light's propagation is the measure of time, clocks run slower in a gravitational field. Since light is also the measure of distance, circular orbits around a massive object will be less than 360 degrees. Gravitational lensing and light bending near massive objects are obvious consequences of the gravitational gradient refractive index.

The interpretation of the meaning of gravitational field may have to be amended somewhat - for instance, my understanding is that inside a massive spherical shell of uniform density, there is no net gravitational force in the conventional sense, nearer portions of the sphere exactly cancelling the attraction of the larger (but more distant) portions of the sphere, yet according to relativity, clocks inside such a shell should still run slower than in free space. I'm not sure that has been verified, but if true, perhaps a scalar rather than vector addition of gravitational fields to calculate the effective refractive index is more appropriate.

It seems possible that the more difficult tensor aspects of general relativity could be mapped onto light polarization/birefringent effects, which also require tensors, but I haven't tried to work out the details.

Here's a random paper on the idea, just to show it isn't crazy, or at least that it isn't original:
<a href="http://arxiv.org/abs/gr-qc/0411034">Effective refractive index tensor for weak field gravity</a>

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Re: 0895: "Teaching Physics"

Postby zackalope » Fri May 06, 2011 9:54 pm UTC

Spacetime is like a party. Where there are large concentrations of people who you interact with, there is more party, and you move more slowly. Where there aren't so many people, there is less party, and you can move more freely.

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Samik
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Re: 0895: "Teaching Physics"

Postby Samik » Fri May 06, 2011 10:22 pm UTC

unus vox wrote:
SirMustapha wrote:
SpringLoaded12 wrote:
Wayfarer247 wrote:Of course, that guy reminds me of people I know who just love to analyze everything. It's a simile, get over it.

He strikes me as the type that overthinks jokes, or points out the flaws and holes in them. I hate that sort of thing.


In other words: don't question the teacher. If you don't understand him, you're dumb.

Weird: when Randall points out that "deurr, if there are no falcons in the Star Wars universe, how can a ship be named the Millennium Falcon??", he's being a pedantic asshole but he's RIGHT; if a student points out a valid flaw in a scientific analogy, which potentially can harm the students' understanding of the concept in hand, he's being a pedantic asshole AND HE'S WRONG.


The best thing about you is how pedantic you get when Randall (who apparently is never tongue-in-cheek or self-acknowledging) appears to be hypocritical. It's like you've stumbled upon a conspiracy. Please go on. /popcorn


Comedic license aside, I think SirMustapha's comparison of the two comics is flawed anyway.

Any model of a system less complex than the system itself is bound to be imperfect. If the student had had a quibble about the use of analogies in general, then he wouldn't have had a problem with being subsequently presented with the equations, which are closer to an accurate representation of the concept being taught than the original analogy. Clearly, this was not the case, so the student's quibble obviously wasn't about the use of analogies as a teaching tool.

But if the student rejects a direct approach, and rejects a circuitous approach, what's left? You either tackle the math head on, or you don't. There's no third alternative for the teacher to fall back on, so he has no choice but to either lose the student's interest, or use a teaching tool that has a "valid flaw".

In the case of the Millennium "Falcon", there are infinitely many possible alternative names that could have been chosen, so there were choices that could be made to avoid the flaw (stronger: there was nothing at all constraining Lando's choice of name).



Just not the same situation at all, really.


EDIT: This is not an endorsement of Etymology. As mentioned in the Etymology thread, the situation appears to have already been addressed.
EDIT2: On the other hand, the alt text states that this was something that bothered Randall as a child. The "Bat-falcon" seems to have been introduced as the namesake in 2008.

charonme
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Re: 0895: "Teaching Physics"

Postby charonme » Fri May 06, 2011 11:33 pm UTC

The rubber-sheet analogy is worthless if it is presented as an explanation of gravity. The space-time distortion story does not "explain" gravity, it just describes its effects in different terms from a different point of view than the usual "massive bodies attract each other" story.

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Re: 0895: "Teaching Physics"

Postby ppaaccoojrf » Sat May 07, 2011 1:55 am UTC

One of my science teachers had a solution for this. The first time someone nitpicked one of his metaphors, he said, 'Ah, yes, that's true. I can see you're paying attention. Was anyone else tempted to make the same observation?'

No one was.

'Very good. So, it looks like you're the only one with that species of brain damage. If you would prefer, I can raise my hand like this every time I'm about to use a metaphor, and you can put your fingers in your ears. That way we can get on with the teaching and you won't hear anything that offends you. Shall I?'


huh.. Not to be nosy but that "solution" has got some serious issues there. First of all, telling your student brain damaged for making a remark is a big no-no. Had I been there I'd have made it more impossible for the class to go on just out of spite (taking into account I hadn't been the one who made the remark. God forbid what I'd done had that happened to me). Teacher's got to seriously revise the way he teaches.

On a brighter note: first post :D

On a heavier (and punier) note: Why hasn't anybody said that space on the x-axis and time on the y-axis gives us the 2-dimensional plane that gravity distorts like in the sheet analogy? Or is that wrong? I always understood that the analogy was that space itself on the x-axis (obviously an approximation to adequate 3D space on 1D) is what's warped along with time, and the straight lines becoming curved are a more appropriate visualization but that doesn't really work with this analogy.That also implies that time is warped one-dimensionally but space 3-dimensionally. So gravity has a more tangible effect on time than it has on space (it gets distributed). Maybe I'm squeezing too much out of the analogy, and would appreciate corrections on possible misconceptions I may have.

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Re: 0895: "Teaching Physics"

Postby KeithIrwin » Sat May 07, 2011 2:17 am UTC

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?


No, this is an explanation of what gravity is. The explanation is used to explain that gravity is caused by the curvature of spacetime. This is Einstein's theory of gravitation. The short version of it is that things fall because anything not acted on by a force moves in a straight line, but straight lines in spacetime lead to massive bodies due to the fact that massive bodies warp spacetime. In his system, gravity is not the result of a force, but the result of the curvature of spacetime and that's what we're using a metaphor to describe.

As for your question of whether or not we fully understand the mechanism, well, of course we don't. No one has ever found a graviton (or likely ever will because there's no actual evidence for their existence). But we don't need to know the mechanism to know that Einstein's theory has proven to be a highly accurate model of the observable phenomenon and in that sense is more correct than Newton's theory of gravitation.

But to get back to the original point, since we're trying to explain -why- smaller things fall towards large bodies, invoking a sheet of rubber and the motion of the smaller body down into the well created by the larger body, the logical question is to ask why the smaller body goes down into the well created by the larger body. The answer, of course, is gravity. If we were just trying to explain what happens, this would be fine, but we're trying to explain why it happens which is where things get circular.

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Re: 0895: "Teaching Physics"

Postby KeithIrwin » Sat May 07, 2011 2:28 am UTC

KrytenKoro wrote:I apologize if I'm mistaken, but isn't the rubber sheet analogy used to explain how gravity ALSO deforms space and time, and not to explain the cause of gravity?


You are mistaken. It's about explaining the cause of gravity according to Einstein's theory of gravity.

snoopy369
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Re: 0895: "Teaching Physics"

Postby snoopy369 » Sat May 07, 2011 5:06 am UTC

I think the teacher just needs a thicker skin. I enjoy explaining scientific concepts using simple metaphors, and people for whom those are too simple can go read the ****ing book if they want to.

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Re: 0895: "Teaching Physics"

Postby philip1201 » Sat May 07, 2011 11:46 am UTC

The kid asks a perfectly valid question. The answer is a constant* vector field tangent on the spacetime plane at rest (which is gravity as it commonly appears to us). It is a good analogy, and I'm surprised the teacher couldn't answer it. In full: "The curvature of spacetime because of gravity is like a rubber sheet on which massive objects distort the sheet because they're being pulled down by the local Newtonian approximation of gravity we commonly experience (With potential energy = mass x "height" x constant of acceleration)."

That said, the kid's attitude needs work, and that is probably the focus of the comic, instead of any faults the rubber sheet analogy may have.

Consumatopia
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Re: 0895: "Teaching Physics"

Postby Consumatopia » Sat May 07, 2011 2:19 pm UTC

The student's phrasing of the question may not be ideal, but the teacher's reaction is not only pedagogically inappropriate, it also completely misses the point. In particular, the student's problem is not that the metaphor deviates from reality, but that the explanation appears circular. All analogies must be approximate, but not all explanations have to be circular.

My guess (as a non-physicist, just going on what I'm seeing in the comic and people's posts here) is that the explanation isn't circular because it's not actually trying to explain what causes large masses to distort space-time, it's using those distortions as an explanation for gravity. Either these distortions are considered simpler than gravity itself, or they also explain other phenomenon, but for some reason "mass distorts space-time" is a simpler hypothesis than "masses pull each other together".

The student should have avoided the interrupting the lecture with an annoying rhetorical question. But the confusion here is actually sincere, and probably broadly shared amongst the class (and readers of the comic like myself).

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Re: 0895: "Teaching Physics"

Postby meatyochre » Sat May 07, 2011 3:21 pm UTC

The point of the comic is that pedantic asshole students who like to think they know more than their teachers should shut the fuck up and ask questions during office hours instead of trying to show how smart they are and wasting everyone else's time.

But all the physics discussion is nice, too.
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Ehsanit
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Re: 0895: "Teaching Physics"

Postby Ehsanit » Sat May 07, 2011 7:51 pm UTC

Now wait a minute. I thought we're meant to be "pretty awesome at teaching"!

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Re: 0895: "Teaching Physics"

Postby Fixblor » Sat May 07, 2011 8:27 pm UTC

Analogies + Asshats = booty booty booty booty rockin' everywhere

"Get it right, get it tight."
... sound advice.
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Samik
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Re: 0895: "Teaching Physics"

Postby Samik » Sat May 07, 2011 8:36 pm UTC

Ehsanit wrote:Now wait a minute. I thought we're meant to be "pretty awesome at teaching"!

We are!

Just... not at learning.

tacvek
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Re: 0895: "Teaching Physics"

Postby tacvek » Sat May 07, 2011 8:37 pm UTC

People claiming that the reasoning is circular are missing the point. The analogy is explaining the big picture (non-linear) effects of gravity in terms of the local (linear, more specifically constant) effects.

For those not satisfied, picture a universe that contains nothing except a small space ship, containing the rubber sheet, and the balls. Obviously there is so little mass in this universe that gravity's effects would not be visible to the naked eye in a short timescale. Now this ship is accelerating at a constant rate ( and the current velocity is well below the speed of light, so special relativity's effect is also negligible). But the sheet will still be distorted. Therefore if you picture the sheet in that ship, rather than here on Earth, you are using regular acceleration to explain gravity.

Basically this is using the equivalence principle to swap out acceleration due to gravity for some other acceleration, which would remove any possibility of circularity.

KeithIrwin
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Re: 0895: "Teaching Physics"

Postby KeithIrwin » Sun May 08, 2011 3:50 am UTC

Consumatopia wrote: My guess (as a non-physicist, just going on what I'm seeing in the comic and people's posts here) is that the explanation isn't circular because it's not actually trying to explain what causes large masses to distort space-time, it's using those distortions as an explanation for gravity. Either these distortions are considered simpler than gravity itself, or they also explain other phenomenon, but for some reason "mass distorts space-time" is a simpler hypothesis than "masses pull each other together".


It's not a simpler hypothesis. It's clearly more complex. But it's more accurate because there are planetary motions which are accurately modeled using this hypothesis which are not modeled as accurately when using Newton's model of gravity. In simple cases, the two hypotheses predict the same results (or results which are close enough that we can't measure the difference between them with existing instruments), but there are situations where they predict slightly differing results. Whenever we have been able to observe those situations, Einstein has been correct and Newton incorrect. That's why we bother trying to explain Einstein's theory of gravity to people rather than just using Newton's theory.

But you'll notice that we do still teach Newton's theory of gravity and his equations in Physics I because they're close enough to correct for most earthly purposes and because they're simpler. We save Einstein's theory for higher level physics courses.

Mental Mouse
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Re: 0895: "Teaching Physics"

Postby Mental Mouse » Sun May 08, 2011 1:44 pm UTC

Jeff S wrote:Ok, I'm going to chime in, because sometimes I'm "that guy". It's not because I'm a wiseguy or trying to cause trouble. It's that I'm trying to *understand*, and the problems in your analogy mean I don't actually understand the situation better than before the analogy.

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?

Also, we live in three-dimensional space. How is the deformation of a 2-dimensional plane analogous to deformation of 3-dimensional space? I can't map from 2D to 3D in this instance, at least not without some additional explanation.


The brief answer to the time issue is that the conversion factor between space and time is c, the "speed of light", and c is huge. The distortions of time corresponding to our local gravity(*) are far too weak for you to perceive by yourself. Indeed, so are the local distortions of space, because it doesn't take much distortion to bend our world-lines(+) hard toward a central mass (see below). However, those distortions do exist -- indeed, the GPS system has to compensate for them, because it actually needs to measure and match up times (between ground and various orbits) precisely enough for the relativistic distortions to matter!

For the 2-D/3-D issue: The point is that there are a lot of things that stay the same, or follow the same rules in 2, 3, or even 4 dimensions, one of those being geometric curvature. For example, as MSTK neglected to note, that Euclidean distance metric works in any number of dimensions -- you add the squares of the distances for however many dimensions you've got, then take the root of the sum. Again, if time is involved, the conversion factor is c, so "1 foot == 1 nanosecond". (That E-mail you mistakenly sent 1.5 seconds ago... might as well be on the moon!)

ETA: So for example, our "32 feet per second per second, moving 16 feet in the first second", implies curving 186,000 miles worth of our world line such that the far end will be 16 feet inward of the near end. That far end is also angled such that if not for the next second's worth of gravity, it would lead to a point another 186,000 miles futureward, and 32 feet inward. Like I said, it doesn't take much distortion... in this case, about 3 parts in a billion.

As I noted above (prior comment), the gravity "inside" the model isn't coming from the gravity around it. The point of the model is that if you have an ant on that classic funnel-curved sheet, which tries to walk "straight" across, the ant's path will curve towards the funnel, and possibly even spiral down the throat. Pushing the model too far beyond that will just get you even more confused.

E_H: Sorry, but that looks suspiciously like a crank theory in classic style. It's got one point of correspondence (light bends! that should have an index of refraction!), but that's about it. As you yourself note, it handles some of the observations for simple cases, but collapses in more complicated cases (like inside a sphere). It might provide a mathematical approximation for some cases -- I note that even your paper restricts itself to "weak field" gravity.

(*) As in, anyplace that's not Way Too Close to a cosmic disaster area.
(+) A "world-line" is the path of anything through both space and time (that is, through the world). All our world-lines run basically past-to-future, tangled a bit from our moving about, but all twisted together into yarn by the rotations and revolutions of our planet.

Lerkistan
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Re: 0895: "Teaching Physics"

Postby Lerkistan » Sun May 08, 2011 9:30 pm UTC

SciBoy wrote: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?


Yes, and no. You can definitely explain something with a simile using gravity without needing to understand gravity (e.g. "How does magnetism work? Think of the magnet lying on a rubber sheet (...)" [not claiming this is an appropriate explanation, it's just an example]). But explaining gravity with gravity? If you think about it, the "rubbersheet" part doesn't add a lot, so the simile really boils down to what this ancient greek philosopher claimed, namely that objects fall down because it's their natural tendency to to that...

hobyrne
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Re: 0895: "Teaching Physics"

Postby hobyrne » Sun May 08, 2011 11:55 pm UTC

Imagine the rubber-sheet experiment being conducted in a spacecraft in outer space, far away from any stars or other bodies. And the spacecraft is accelerating, 'upwards'. What was, in the previous experiment, gravity pulling the balls 'down', is, in this experiment, the inertia of the balls resisting the acceleration.

If the universe is expanding at an accelerating rate, then a small patch of it will look like the sheet in the spacecraft. The model shows a direct link between inertial mass (how difficult it is to move something) and gravitational mass (how much it attracts other bodies).


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