Can One Grasp Relativity Without Doing the Math?

[Uncayimmy]

Sure, but the point stands that they are really geometery, so you could show a lot of it with out numbers or equations.

I'm not clear how you show the twin aging less using geometry.

 

[sol invictus]

I'm not clear how you show the twin aging less using geometry.

You think of Lorentz transformations as "rotations" through a complex angle. It works nicely, although of course it's completely equivalent to the standard algebra.

 

[Almo]

Woa. Those videos are clear.

 

[mhaze]

The question is in the subject: Do you think relativity can be grasped without doing the math? ....

Yes, I think so, but you'd need a REALLY BIG HAND. Like, if you went to sling a ball around, maybe that ball was a planet. Then throwing a fast ball, the darn relativity stuff'd increase the mass of the arm, hand and the ball, and if they got big enough, that'd knock you in the head, and you'd begin to grasp it...

Also, if you just picked up a bunch of the stars, sort of like picking grapes, then squeezed them together into one big mess, then you'd see them all start to get sucked into a black hole, and you'd start to gra-

 

[Brian-M]

In what direction could the Earth accelerate to provide a gravity-mimicking force everywhere on the surface?

Given that the Earth's surface faces all directions at once, the Earth would have to accelerate in all directions at once. It's kind of an odd thought.

But then again, isn't this sort of what the Earth is doing in curved space-time? The mass of the Earth distorting space so that the surface of the Earth is sort-of accelerating outwards in order to remain in the same position with everything else?

(I put that very badly, and I'm probably very wrong. )

 

[ferd burfle]

Seconded. His descriptions in one of the early chapter in The Elegant Universe are about as good as one can get without math.

Thanks for the reference, folks, I'll look for this the next time I get to a bookstore. Although it's probably somewhat out of date now, I liked Martin Gardner's Relativity Simply Explained. I struggled with college math but I like to think I understand most of the basics conceptually. What I'm sure of is that I couldn't apply any of it without knowing and using the math. And while I may not be able to follow the arguments in detail, the less math used by a poster who comes by here with an "Einstein was wrong" pitch, the more quickly I become convinced of their crankitude.

ferd

 

[Kahalachan]

You can do the math no problem, but it can still be hard to fathom.

Math lets you do work with dimensions higher than 3 spatial dimensions, but I can't visualize it.

So even understanding relativity in a mathematical sense doesn't mean our naive intuition can fully grasp it.

 

[sol invictus]

You're probably right, but I still have this mental picture of the researcher in the lab seeing that the field lines are not parallel and not radiating from an axis, and therefore concluding that no kind of acceleration could be behind them, meaning that they must be due to gravity. Maybe there is in general some really complicated way of accelerating the lab to replicate the effects of gravity from any specific mass. I don't see how, though.

You can't simulate mass with acceleration alone (mathematically speaking, flat space has exactly zero curvature no matter what coordinates you use). But if both mass and acceleration are present, I don't think they can be disentangled in general. In fact I'm not sure there's even a well-defined distinction.

It's actually an interesting question.

A couple of animations I did about five years ago for the NSF (the Earbot.com URL was pasted on by whoever posted them on youtube; I have no affiliation). Minimal math, but I still found it necessary, even if I'm only using a geometric explanation:

Very good. Thanks for posting them.

 

[ponderingturtle]

I'm not clear how you show the twin aging less using geometry.

That is easy, you look at the premises. The conditions only hold for inertial reference frames. The accelerating twin is accelerating and thus not an inertial reference frame.

 

[Ziggurat]

Global measurements don't help (except in special cases). Try this: I give you two metrics. That's complete information about the spacetime, far more than you could ever hope to get from measurements. Your job is to tell me if they describe the same configuration of matter. If you cn distinguish gravity from acceleration that should be easy, but AFAIK there is no known way to do it.

Can you give me two different matter configurations (or more precisely, mass/energy configurations) which can produce the same metric? Can you give me an acceleration metric which matches a mass metric globally? I don't think you can, even for any special cases.

 

[Dorfl]

You can't simulate mass with acceleration alone (mathematically speaking, flat space has exactly zero curvature no matter what coordinates you use). But if both mass and acceleration are present, I don't think they can be disentangled in general.

So, for example, I'd be unable to tell a point mass below a non-accelerating lab from a point mass slightly further away accelerating with the lab? I can buy that.

 

[Uncayimmy]

That is easy, you look at the premises. The conditions only hold for inertial reference frames. The accelerating twin is accelerating and thus not an inertial reference frame.

You think of Lorentz transformations as "rotations" through a complex angle. It works nicely, although of course it's completely equivalent to the standard algebra.

To be clear, I'm not trying to pick a fight here...

I know both statements are brief, but to me they don't make sense or at least are not helpful. That doesn't mean they are wrong. To me it brings up a problem we all suffer when we know a subject very well and are trying to explain it to others who don't get it. Do these examples and thought experiments make sense to those who don't actually get it in the first place?

 

[ben m]

To be clear, I'm not trying to pick a fight here...

I know both statements are brief, but to me they don't make sense or at least are not helpful. That doesn't mean they are wrong. To me it brings up a problem we all suffer when we know a subject very well and are trying to explain it to others who don't get it. Do these examples and thought experiments make sense to those who don't actually get it in the first place?

I believe sol and ponderingturtle are answering different questions. Sol is answering "how do you do a Lorentz transformation graphically". Ponderingturtle is answering "how can you tell that the twins aren't identical in the twin paradox". So, yes, they're a bit hard to understand.

I think the answer you are looking for is "To measure times graphically, remember that a space-time diagram has time on the Y-axis. For any line, the vertical component tells you how much time elapses between events in the currently-drawn rest frame. So it's easy to read times off the graph"

 

[Vorpal]

Find the set of geodesics of your spacetime. Any trajectory that deviates from them, including the coordinate curves, is accelerated. But there's a bit of a sleight of hand here, and that the point is physical rather than mathematical. The metric equivalence problem is irrelevant to it (I don't think it was solved for Lorentzian manifolds, although it was for Riemannian ones... but if it was, it would conceptually change little).

The principle of equivalence erases any intrinsic distinction between gravitation and inertia--if it were not so, then there would be something within spacetime that couples to mass, and a purely geometrical theory would be impossible. However, what tells you the inertia is not the curvature, but the affine connection, meaning it is improper to think of flat spacetime as the absence of a gravitational field. Absence of curvature, surely (by definition), but not absence of inertia, and hence not gravity. (That's not to say curvature isn't important--but that's an invariant of the connection, not the connection itself.)

So in coordinates,
'gravitational field components'='inertial field components'='connection coefficients',
and it no longer makes much sense to separate acceleration from gravity at any level. Even in flat spacetime, say in a rotating reference frame, "my coordinates are curved" becomes equivalent to "there's a gravitational field curving things."

 

[Uncayimmy]

I think the answer you are looking for is "To measure times graphically, remember that a space-time diagram has time on the Y-axis. For any line, the vertical component tells you how much time elapses between events in the currently-drawn rest frame. So it's easy to read times off the graph"

You lost me. Aaargh! Check out this diagram from another thread:

If I look at the Y axis as being time, then when the twins meet up again, they do so at the same time because they are at the same point on the Y axis. Based on the way your statement is written, I would expect that when all three lines intersect, they will measure the same amount of time as having elapsed. However, that's not the case, is it?

If only I would sit down and do the math....

 

[roger]

Sol, so you are telling me you do not know if the reason you are sitting in your chair without floating off is because of the Earth's gravity or not?

Yes, I understand mathematically equivalent. I'm pointing out there is a huge mass under your butt, there is a huge mass under the person's butt on the opposite side of the globe, and you are both being pulled towards the center of that mass.

 

[sol invictus]

Can you give me two different matter configurations (or more precisely, mass/energy configurations) which can produce the same metric?

No (by definition more or less), but I can give you two metrics for the same matter configuration, which is more to the point.

Can you give me an acceleration metric which matches a mass metric globally? I don't think you can, even for any special cases.

Not a pure acceleration metric, no. I'm talking about cases where there is some of "both".

So, for example, I'd be unable to tell a point mass below a non-accelerating lab from a point mass slightly further away accelerating with the lab? I can buy that.

Perhaps, yes. Actually I wouldn't be surprised if any matter configuration could be mimicked so long as you don't have information about a closed surface surrounding any of the energy, but I'm not sure about that.

However, what tells you the inertia is not the curvature, but the affine connection, meaning it is improper to think of flat spacetime as the absence of a gravitational field. Absence of curvature, surely (by definition), but not absence of inertia, and hence not gravity. (That's not to say curvature isn't important--but that's an invariant of the connection, not the connection itself.)

Physicists make the distinction largely because there is a parameter, Newton's constant G, that determines the strength of gravity's coupling to matter, but not the resistance of mass to acceleration. In other words one could set G=0 and live in a world with no gravity (i.e. always flat), but with inertia.

But I understand your point, and in fact I think it's a better way of looking at it.

Sol, so you are telling me you do not know if the reason you are sitting in your chair without floating off is because of the Earth's gravity or not?

Yes, I understand mathematically equivalent. I'm pointing out there is a huge mass under your butt, there is a huge mass under the person's butt on the opposite side of the globe, and you are both being pulled towards the center of that mass.

In practical terms one often does know, as on the surface of the earth. But consider this: the force you feel is only partially due to the mass of the earth - there is also the acceleration due to the rotation, due to the sun and moon, etc. If you didn't have other evidence (like being about to see the earth) you might have quite a bit of difficulty untangling all that.

 

[Raze]

It's actually easier to understand with the math, once I took the time to learn it (it's simple algebra).
Prior to that, I'd 'understand' it while reading the non-math explanations, like Brian Greene's. Then an hour later, I couldn't explain it to myself, let alone someone else.

http://meshula.net/wordpress/?p=222

They really need to put in some of the steps solving for t'. Even people who passed basic algebra will be intimidated because they aren't used to working exclusively with variables. Recently I noticed this in another forum, where solving for an unknown variable with respect to other variables was like breathing for me, and I couldn't figure out why the people I was explaining the thing to couldn't follow, even though they could solve for, say, x in

16x² = 64 (9) + 25 (4),

which of course is almost identical in form to the equation solved in your link, except instead of a few variables squared there are numbers squared.

What I'm saying is, sure, many people won't get the math, but people trying to explain physics to laymen need to go slower and show more steps in any math they want to present to laymen. Things you've worked with for years will seem very natural to you, and often times you won't even realize that other people are lost immediately after step 1.

 

[sol invictus]

In other words one could set G=0 and live in a world with no gravity (i.e. always flat), but with inertia.

Let me amend that slightly. One can take the limit G->0 while keeping the background fixed. In other words G=0 implies that the background is completely rigid and does not change as a result of energy moving around, but it does not necessarily imply that it is flat.

Distinguishing "gravity" from "acceleration/inertial forces" in such a theory is particularly problematic...

 

[ben m]

You lost me. Aaargh! Check out this diagram from another thread:
[qimg]http://www.internationalskeptics.com/forums/imagehosting/thum_119246901a635fa02.gif[/qimg]

If I look at the Y axis as being time, then when the twins meet up again, they do so at the same time because they are at the same point on the Y axis. Based on the way your statement is written, I would expect that when all three lines intersect, they will measure the same amount of time as having elapsed. However, that's not the case, is it?

If only I would sit down and do the math....

Don't worry, you're almost there! The y-axis is "time" as measured in the reference frame drawn. The left ddrawing, for example, is the reference frame of the Earth observer. Let's note that the "turnaround" event is 1cm up from the "departure" event, and the "arrival" event is another 1cm up from that. So this observer will say that 1 yr elapses between departure and turnaround, and 1 yr elapses between turnaround and arrival. That's on the observers's clock only.

The middle diagram has the y-axis representing "time" as measured in a ship departing to the right. This is the frame in which the B-ship is at rest during its departure cruise, so this tells us how clocks aboard the B-ship are behaving. How much time elapses on this clock between the "departure" and the "turnaround" events? Much less than 1cm---looks like maybe 5 mm. (This is the short, vertical blue line.) So these clocks advance only 6 months.

After the turnaround, the B-ship is in a different rest frame; you can measure times in this frame using the right-hand diagram. How much time advances on a clock in the new B-ship frame, between turnaround and departure? Looks like another 5mm-long vertical blue line. So this clock advances another 6 months.

So, in the Earth frame (left diagram) our rest clock advanced 2 years between arrival and departure. In the B-ship's two frames, we advanced a total of only one year, half in the departure frame ( middle) and half in the return (right.)