Question about gravity

[Fredrik]

I don't have a problem with "curvature"; that's a commonly understood word, and can generally be related to, but "space-time curvature", what does that look like?

It isn't possible to get a mental picture of it, for two reasons:

a) Space-time is four-dimensional, and we can only picture three.

b) When we picture a curved two-dimensional surface, we always picture the curvature as a deformation into a third dimension, but the space-time manifold is curved without being deformed into a fifth dimension.

That's why you need differential geometry to define what curvature means.

This is one way of explaining a small part of it in plain English: Imagine transporting a tangent vector along a very short closed curve while trying to keep it pointing in the same direction. If the tangent vector isn't pointing in the same direction when you get back, and that effect persists when you shrink the loop to zero length, then the space-time manifold is curved at that location.

Unfortunately that doesn't explain what a manifold is, what a tangent vector is or what it means to keep a tangent vector "pointing the same way" and it doesn't tell us how large the curvature is. Differential geometry explains all of those things.

I understand, but the theories of relativity, or our understanding of gravity, the way you explain it, seems like one entire axiom.

I guess you can say that it is. That "axiom" (or whatever we should call it) is what defines the theory. Everything else is derived from it. But this is how it is with any theory. The axioms define the theory, and you use them to derive everything else.

I could go into some detail about how the theory is used. For example, suppose we want to know what GR says about the behavior of matter in the universe on very large scales. First we note that on large scales matter is distributed very uniformly across the universe. So we decide to insert a completely uniform distribution of matter into the right-hand side of Einstein's equation, and see what comes out of the left-hand side. We find three solutions, all of them describing an expanding universe. All of them have a "big bang" singularity in the past. One of them says that space is finite and that the universe will end in a "big crunch". The other two say space is infinite and will expand forever.

That's usually how it's done. Decide what kind of matter distribution you're interested in, insert an idealized version of that into the right-hand side and see what comes out of the left-hand side. The result should be an approximate description of what you're interested in.

You could do it the other way too: Decide what kind of space-time geometry you'd like to study, insert it into the left-hand side, and see what kind of matter distribution comes out of the right-hand side. This is how you'd have to do it if you e.g. want to know what GR says about sci-fi stuff like time travel, wormholes and warp drives.

 

[Southwind17]

Does anybody know whether Einstein ever formulated a Theory of Retail Relativity, and if so whether it supplants Reilly's Law of Retail Gravity, or was high street shopping simply not so sophisticated in Einstein's time?!

 

[The Man]

That is an outstanding claim. Extraordinary. Can you provide us with the source of this extraordinary claim? Because if you can't, I am going to mock you too.

Mock all you want, it won’t change a thing. Try looking up the Scientific method. It refers to the validation of hypothesis and theories not adherence to “laws”.

http://en.wikipedia.org/wiki/Scientific_method

The unmitigated adherence to perceived physical “laws” is the path of pseudoscience.

In the real world we call adherence to the laws of physics things like, science, engineering, and reality. I don't know what planet you live on, but it can't be Earth. Here we have to obey the laws of physics, and depend on them to get things done.

http://en.wikipedia.org/wiki/Physical_laws

Physical laws are distinguished from scientific theories by their simplicity. Scientific theories are generally more complex than laws; they have many component parts, and are more likely to be changed as the body of available experimental data and analysis develops. This is because a physical law is a summary observation of strictly empirical matters, whereas a theory is a model that accounts for the observation, explains it, relates it to other observations, and makes testable predictions based upon it. Simply stated, while a law notes that something happens, a theory explains why and how something happens.

Appling theories, or explanations of how and why things happen, are what we depend on “to get things done” not the “summary observation of strictly empirical matters”.

Violations (or rather, attempts to violate) the laws of physics, results in much suffering.

http://en.wikipedia.org/wiki/Physical_laws

Those laws which are just mathematical definitions (say, fundamental law of mechanics - second Newton's law ), or uncertainty principle, or least action principle, or causality - are absolutely correct (simply by definition). They are extremely useful - because they can not be violated nor falsified. .

Such mathematical definitions are an important part of science just as mathematics is in general. However, science is not limited to or based only on such mathematical definitions and the scientific method specifically requires the effort to falsify conjectures. Even such mathematical definitions sometimes require the clarification of theories in order to maintain the mathematical validity of that definition. For example Newton’s second law that force equals the change in momentum divided by the change in time was formulated before the advent of special relativity. With special relativity the equation takes a different form with additional factors to maintain its validity at relativistic speeds.

http://en.wikipedia.org/wiki/Newton's_law

A verbal equivalent of this is "the acceleration of an object is proportional to the force applied, and inversely proportional to the mass of the object". If momentum varies nonlinearly with velocity (as it does for high velocities—see special relativity), then this last version is not accurate.

http://en.wikipedia.org/wiki/Physical_laws

Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies can be said to generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations (see below), to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g., very large or very small scales of time or space, enormous speeds or masses, etc. Thus, rather than unchanging knowledge, physical laws are actually better viewed as a series of improving and more precise generalizations.

Violation of a less precise generalization, or physical law, results in a more precise generalization or physical law. The only suffering results from considering all physical laws as un-falsifiable, unchanging knowledge and not improving.


So, mock and suffer as much as you please and your knowledge of physical laws will remain unchanged. Science continues improving and does not suffer the limitations of unchanging generalizations or the mocking of those believing all physical laws to be unchanging mathematical definitions and without the possibility of invalidation.

 

[MattusMaximus]

That's why you need differential geometry to define what curvature means.

"Differential geometry" -- ah, the joy of tensor calculus. For those interested, this level of mathematics is like combining all of the following into one gooey mix... differential equations, multivariable calculus, and linear/matrix algebra.

If you've had any exposure to those forms of mathematics, you'll get a rough idea of what differential geometry is like. It's special

Unfortunately, since the math is so damn hard, it makes much of general relativity inaccessible to most people. Damn shame, because it's soooo cool!

Cheers - Mattus

 

[MattusMaximus]

I don't have a problem with "curvature"; that's a commonly understood word, and can generally be related to, but "space-time curvature", what does that look like?

Here's a good way to start looking at it...

http://www.theory.caltech.edu/people/patricia/st101.html

There's a little bit of math there, but the layout and explanations are pretty good.

Cheers - Mattus

 

[Southwind17]

Here's a good way to start looking at it...

http://www.theory.caltech.edu/people/patricia/st101.html

There's a little bit of math there, but the layout and explanations are pretty good.

Cheers - Mattus

This is interesting Mattus - thanks. I've also just read this interesting historical article, and am part way through reading Einstein's theories themselves.

Unfortunately, and call me dumb, if you like, but I'm no nearer understanding what's keeping me seated in my chair as I type this! Do we really need to wander off into the cosmos at close to the speed of light to try to do that?!

 

[Molinaro]

How can everybody be so dumb?

Actualy, it's just you.

But thanks for the laughs. It realy is one of my favorite things to laugh at -- dumb people with the 'just a theory' line.

 

[Tokenconservative]

Don't know nutin' 'bout no gravity...but here's a funny story about it.

I worked part time for a bit in a large computer store when the PC (not to dis you Apple folks...like, kleenex, or zipper...) boom was full tilt in the mid-90s.

They guy who worked behind the upgrades desk was this really deadpan sort that would have me ROTFL before this was even a widely accepted term in our culture.

Anyway, a customer comes up to him, holding an UPS (uninterptable power source) and asks him, "how will gravity affect this?"

To which this smart ass replied by saying, "I dunno, let's see." He grabbed it out of the guy's hand and dropped it on the floor from about shoulder height.

Then, he looked at the guy and said, straightfaced, "Gravity works on it just fine."

I was laughing so hard I had to leave the sales floor for about 20 minutes and every time I saw the guy for the next week I would bust out laughing.

Tokie

 

[Skeptic Guy]

Been too busy at work to respond before now, but:

Have you ever heard of the "inverse square law"? It isn't considered "the inverse square theory", and if you were to talk about it like that, you would be considered uneducated.

Same for many other laws. Here is a list
http://en.wikipedia.org/wiki/Scientific_laws_named_after_people

sometimes they are called "equations", "principles", or "functions". But nobody who is educated in science would try to tell you that they are only theories, and we can never get any closer than a theory, in regard to understanding the real world, and the forces in it.

I think that you are suggesting that a scientific "law" is more important than a scientific "theory", which isn't necessarily the case.

In order of importance to Scientists:

1) Theories
2) Laws
3) Hypotheses
4) Facts

Laws [such as Newton's inverse square law - see I are educated!] are extremely useful empirical generalizations: they state what, under certain conditions, will happen.

However, laws may not hold under certain conditions.

Laws are "descriptive generalizations" but rarely explain natural phenomena. That is the role of a "theory".

Therefore scientists place theories on top of the hierarchy of explanation.

The theory of gravity is much more descriptive and explanatory than any law may be.

The naive belief that we are never certain about anything, is sometimes trotted out to make some kind of bizarre point, usually that we can never know anything, we only have theories and stuff. It just isn't true.

I never stated that.

The most important part of science is the experiment, not the theory.

The experiment is important in the sense that it builds up evidence to support a theory.

I've had this discussion before, and if you want to argue that there are no laws, only theories, go right ahead. But after this attempt to enlighten you, I'm only going to mock you, not try and educate you.

Which for a critical thinker involved in a rational discussion on an educational forum...makes a lot of sense.

 

[MattusMaximus]

Unfortunately, and call me dumb, if you like, but I'm no nearer understanding what's keeping me seated in my chair as I type this! Do we really need to wander off into the cosmos at close to the speed of light to try to do that?!

No need to call anyone "dumb" - relativity is a royal pain to understand, because humans didn't evolve with the experience of traveling half the speed of light or inside ultra-intense gravity fields, etc. Wrapping one's mind around the reality of relativity and how it influences our view of the cosmos can take a long time - hell, I've got an advanced degree in physics and I still struggle with it!

Also, be careful about mixing up the two aspects of relativity theory: special and general relativity (or SR and GR). SR is the kind that deals with high-velocity motion, what most people think of when talking about relativity. GR is the much more mathematically complex part of the theory that deals with gravitation.

In my effort to understand general relativity (did I say it was waaay tough?) I decided a few years ago to teach myself the basics. Even with my advanced degree and graduate training, it took me almost six months to learn the basic tenets of GR. I first had to teach myself basic tensor calculus, which is like shoving one's head through a cheese grater

My advice: keep reading and keep asking questions. It is a slow and painstaking process to get to the point where you can really start to gain some level of understanding on this stuff. You can get a decent grasp on SR with an understanding of basic algebra & geometry, but to go any further than that you'll need much more math under your belt.

To assist in more detail, I'll post some more links and a good way to go after the subject of SR in a bit. Stay tuned.

Cheers - Mattus

 

[MattusMaximus]

It realy is one of my favorite things to laugh at -- dumb people with the 'just a theory' line.

For those who think that general relativity is "just a theory", they should throw away all of the following kinds of technology which work based, in part, upon the principles of GR:

GPS receivers
satellite phones
Weather.com
all satellite-based communication

Unless they volunteer to do away with such "heretical" technology, they can be appropriately labeled as hypocrites, in my opinion.

Cheers - Mattus

 

[MattusMaximus]

Here's the way I present the topic of special relativity (SR) to my students:

1. Convince them of the invariance of lightspeed in vacuum. That is, tell them that, despite our everyday experiences with cars, jets, and whatnot, the speed of light in a vacuum is measured by all observers - regardless of their relative velocities - to be the same (3x10^8 m/sec). As I said, this seems amazingly counter-intuitive, but it is a confirmed experimental fact of nature. It was first proved in 1887 in the famous Michelson & Morley Experiment that attempted to measure the shift in lightspeed as the Earth moved through the "aether"...

http://en.wikipedia.org/wiki/Michelson-Morley_experiment

Once my students can, at least in principle, begin to accept the constant nature of lightspeed, then I move on to the implications of that fact.

2. Time Dilation: if you can accept that lightspeed is the same in all frames of reference for all observers, you quickly get to the "good stuff". In a famous gendanken (thought experiment), Einstein thought about a train flying along a straight track at high speed. Imagine there are two observers: one riding on the train and one on the ground watching the train go past them.

An experiment is now performed: the observer on the train "throws" a beam of light towards the ceiling, where a mirror rests. Now, both observers time how long they perceive the light to travel to the ceiling, bounce off the mirror, and return to the starting point.

Result: the observer on the ground will notice the light traveling along a longer path than the observer on the train. And since both will agree on the speed of the light beam, then because the ground observer sees it move over a longer distance they must also see it taking a longer time to do so...

speed = distance / time <--- to keep this speed constant for a longer distance, the time of flight for the light beam must also be measured as being longer.

For a good picture representing this scenario, check out this link:

http://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation

Therefore, time is measured to pass more slowly on clocks that move relative to you. Note that "clock" is defined as anything which measures the passage of time: traditional clocks, atomic decay rates, aging, etc. Also, please note that this phenomenon of time dilation due to high relative speeds is well documented. Scientists who use particle accelerators notice the effect all the time - I even have my students perform a simple, table-top experiment that confirms time dilation - coolest thing ever!

Any questions so far?

Cheers - Mattus

 

[Southwind17]

Therefore, time is measured to pass more slowly on clocks that move relative to you. Note that "clock" is defined as anything which measures the passage of time: traditional clocks, atomic decay rates, aging, etc. Also, please note that this phenomenon of time dilation due to high relative speeds is well documented. Scientists who use particle accelerators notice the effect all the time - I even have my students perform a simple, table-top experiment that confirms time dilation - coolest thing ever!

Any questions so far?

Cheers - Mattus

Just one: What's this "cool" table-top experiment?!

 

[robinson]

I wondered the same thing!

 

[Skeptic Guy]

link

Excellent.

 

[MattusMaximus]

Just one: What's this "cool" table-top experiment?!

Measuring the lifetime of muons as they are captured inside a device called a scintillator. Because they are moving through our atmosphere at roughly 0.9952c (c is the speed of light), they have a lifetime of about 10 times as measured from a frame of reference at rest with respect to the muons.

Read more about this kind of experiment here...
http://teachers.web.cern.ch/teachers/archiv/HST2000/teaching/expt/muoncalc/lifecalc.htm

And here's a picture of the apparatus - the oscilloscope on the left reads off when muons hit the detector (aka "scintillator") which is the big green drum on the right...



As I said, coolest experiment the students do all year. And they never stop talking about how awesome it was - it's enough to bring a tear to my eye

Cheers - Mattus

 

[Southwind17]

Measuring the lifetime of muons as they are captured inside a device called a scintillator.

Damn! I thought it was going to be something I could do myself with a bowl of water, aluminium foil, bicarbonate of soda and a stop watch or such like. Now that would be worth talking about!

 

[MattusMaximus]

Damn! I thought it was going to be something I could do myself with a bowl of water, aluminium foil, bicarbonate of soda and a stop watch or such like. Now that would be worth talking about!

Sorry, not quite so simple as all that. It'd be nice if it were though, because coming up with a table-top experiment to show my students time dilation from relativity took quite some time.

Now if I could only get that experiment displaying the photoelectric effect working...

Cheers - Mattus

 

[ponderingturtle]

Sorry, not quite so simple as all that. It'd be nice if it were though, because coming up with a table-top experiment to show my students time dilation from relativity took quite some time.

Now if I could only get that experiment displaying the photoelectric effect working...

Cheers - Mattus

Cool, the only relativistic confirming experiment I remember doing was compton scatering. And that does not demonstrate time dilation but reletivistic energy and momentum issues.

 

[tony soprano]

Very informative thread. Thank you all.