Universal Gravitation: Einstein's Warping of Space and Time

[Pete81t]

I'm new to the physics forums so correct me if I'm in the wrong place. We started a new unit on universal gravitation in my physics class, and I'm not sure I understand the following passage from the beginning of the chapter:

"Albert Einstein made the amazing discovery that gravity arises from the 'warping' of space and time. Neither space nor time is perfectly smooth. Both are just a tiny bit lumpy."

What exactly does this mean?

 

[Parlyne]

It means that either the textbook author doesn't really understand general relativity, or is trying very hard to avoid explaining it. That said, if the chapter is really on Universal Gravitation, you don't really need to worry about Einstein, as long as you keep in mind that the law of gravity you're being presented is only strictly true in the "weak" gravity limit. (Of course, any gravitational force you feel in your life will be weak by those standards.)

 

[pibomb]

The author of your book seems to misunderstand that the spacetime of general relativity is flat. The only lumpiness I can think of are ground state fluctuations.

Like Parlyne said, you shouldn't need to worry about Einstein too much because universal gravitation is under Newton and seldomly touches Einstein with detail.

 

[Pete81t]

Alright, in that case I'll put Einstein aside for now. But the author of the book is a guy by the name of Paul Hewitt, and I was under the impression that he has a real knack for physics, so I'm a bit surprised he might have erred or misunderstood such a concept.

 

[Parlyne]

The "warping space and time" comment is exactly true. The "lumpy" thing, however just doesn't make any sense.

It's possible that he doesn't have that good an understanding of general relativity. Many physicists who work in significantly different fields don't. Or, he could just be trying to side-step the issue.

 

[Stingray]

The "warping space and time" comment is exactly true. The "lumpy" thing, however just doesn't make any sense.

"Lumpy" just means that spacetime isn't flat. It's a reasonable choice of words in my opinion. But describing what that means in much detail takes a lot of effort...

 

[rcgldr]

I'm a bit concerened about "cause and effect" here. Warping and spacetime are the cause, and gravity is the effect ("gravity arises...")?

A few threads on this seem confusing to me.

My understanding is that gravity is an attractive force and that it also affects times (as gravitational field strength increases, time slows down). I'm not clear on the relationship between the warpage of space (at least in 3 dimensional space), and gravity.

My point is that mass is the cause, and gravity and the other stuff are the effects. One is an attractive force we call gravity. With repect to gravity, there are 3 different and independent (in my opinion) effects: an attractive force, the slowing of time, and the warping of space (again I ask is this a warping of 3 dimensional space, or does the warping only occur in a higher dimension?). Now who can really state if the slowing of time and warping of space is related to gravity or related to the presence of mass?

The slowing of time can occur due to acceleration to a high speed, and remain slow while traveling at at a high speed. Is this because of the speed of the object, or because of it's relativistic increase in mass?

 

[Chris Hillman]

Warning! Warning! And a reading recommendation

Hi Pete,

I don't think the description you quoted is so awful for a unit on universal gravitation, so I'd advise you not to get all worried :-/

The author of your book seems to misunderstand that the spacetime of general relativity is flat.

Oh my. I am surprised that no-one (apparently) has yet objected to this statement, since it is, if you will pardon the pun, flat out wrong. At least, under the reasonable assumption that by "flat" pibomb means "vanishing Riemann curvature tensor".

(After discarding several possible guesses about what pibomb could have been thinking, it finally occurred to me that perhaps he/she was thinking of the -Ricci- curvature tensor. However, a four dimensional Lorentzian manifold with vanishing Ricci tensor but nonvanishing Riemann tensor is generally called "Ricci flat", or in the context of gtr, "a vacuum solution". However, even this modified claim would only describe correctly -vacuum- solutions, not spacetime models including some dust, an electromagnetic field, or whatever.)

Pedantic quibbles: the Minkowski spacetime is indeed flat and it is trivially a vacuum solution to the Einstein field equation (EFE), and even curved spacetimes might have nonzero curvature in some region (for example, a model of a thin uniform density spherical shell), so it is probably best to say that "spacetime models in gtr generally have nonzero Riemann curvature at most events".

The "warping space and time" comment is exactly true. The "lumpy" thing, however just doesn't make any sense.

Parlyne, I think you are being rather harsh! I agree with stingray: while the quotation from the textbook was taken out of context, if for example you are discussing something like a galaxy full of main sequence stars, on a suitable length scale, "lumpy" might not give such a bad first approximation to the general idea of how gtr treats gravitation.

My understanding is that gravity is an attractive force and that it also affects times (as gravitational field strength increases, time slows down).

Well, saying that "time slows down" makes no sense at all, when you think about it, and of course gtr says no such thing. Rather, it represents the gravitational field as the curvature of spacetime itself. A fundamental feature of curved manifolds is the fact that a pair of initially parallel geodesics (analogue of straight lines in euclidean space) may diverge or converge as you run along the pair. To understand what gtr really says about "gravitational time dilation", let's consider a simple thought experiment:

Let us imagine two observers in two rocket ships who use their rocket engines to hover motionless at two radii $$r_1, \, r_2$$ where $$r_2 > r_1 > 0$$, over a massive object. Suppose that the closer observer is sending out time signals every second (by his clock) to the farther observer. You can picture the "world lines" of these signals as "null geodesics". As it happens, the vacuum field equation of gtr dictates in this situation that radially outgoing null geodesics must diverge, so that the farther observer finds that according to HIS clock, the signals are arriving at intervals longer than one second.

Another manifestation of essentially the same effect is the so-called "gravitational red-shifting" of light signals: if our close observer fires a laser with frequency $$\nu$$ at the farther observer, its frequency as measured by the farther observer will be smaller than expected.

Notice that time certainly has not slowed down anywhere in this picture!

If you are curious to learn more, you might enjoy the excellent popular books by Robert Geroch and by Robert Wald (both leading experts on gtr work in the same department at the University of Chicago, as it happens) listed at ttp://www.math.ucr.edu/home/baez/RelWWW/reading.html#pop

Chris Hillman