xkcd

by **Tupolev** » Sun Oct 09, 2011 2:14 am UTC

Okay, it's been a while since I've looked at relativity, and I need a sanity check.

I was trying to reassemble, in my mind, in intuitive terms, ways in which causality issues pop up due to FTL objects, and I'm not sure that I still have a grasp on it.

So, I was thinking about what problems would result from "teleporting" a message between two observers (i.e., transmitting the message so that, in the reference frame of the sender, it arrives at exactly the same time as it's sent). Anyway, suppose that the two observers (let's say P1 and P2) are travelling extremely fast toward each other (not FTL, but still fast). And suppose P1 teleports a message (let's call it message A or MA) to P2. I seem to recall that, in this case, from P2's perspective, MA would arrive prior to P1 having sent it. And then let's suppose that P2 teleports a response (let's call it MB) immediately after receiving MA. So, this time, it's P1 who perceives MB as having been received prior to being sent, since the sending and receiving of MB was simultaneous in P2's frame. So, according to P1, since MA was sent instantaneously, and since MB was sent when P2 received MA, and since P1 received MB prior to P2 sending it, P1 actually receives MB prior to sending MA, which is, causally speaking, kind of weird.

I also imagined the situation in terms of rough two-frame spacetime graph, which I hope I remembered how to use, where P1 is the black reference frame, P2 is the red (slanted) reference frame, and the green arrows represent the two teleportations of the message.
http://i.imgur.com/eVt1f.png

Does it look like I'm vaguely on the right track here?

Thanks.

by **Robert'); DROP TABLE *;** » Fri Oct 14, 2011 11:50 am UTC

I've heard of the phenomonon of gravitational lensing, and it seems a very intuitive idea that a mass will lens light in that way. However, I also heard that, unlike in an optical lens, when the light reaches the focal point, it doesn't then diverge and go out of focus again. Can anyone explain how this could be true, if it is?

by **Goemon** » Sun Oct 23, 2011 3:35 pm UTC

The center of an ordinary optical lens bends light passing through it the least, while the edges bend light the most. This concentrates all the light passing through at a single point behind the lens.

A gravitational lens does the opposite: the light passing closest to the center of the "lens" is bent the most, focused on a point immediately behind the "lens", while light passing farther from the center bends less, focusing on a point farther away. The result is that the gravitational lens concentrates the bent light all along a line behind the "lens", rather than at a single point.

by **flamewise** » Thu Nov 03, 2011 10:47 am UTC

As a wary newcomer to this thread, would this be the place to ask what the best way is to measure the actual speed of light (or, if you like, the length of the meter)?

Apparently, almost all methods require a perfect vacuum. But how do you create a perfect vacuum with neutrinos zipping through everything? Or can you just disregard those because their mass is so little?

What about neutrinos themselves? Would they slow down when going through thick stuff? Then you couldn't just measure their speed instead either.

Maybe you could convert mass to energy and get it from E = mc² - this doesn't appear to require a vacuum.

by **eSOANEM** » Thu Nov 03, 2011 12:47 pm UTC

There are lots of equations using c that don't refer to how fast light moves specifically. Any of these equations can be used to calculate the value of c, for example, this can be done the time dilation of a moving clock with respect to a "stationary" one.

by **Robert'); DROP TABLE *;** » Thu Nov 03, 2011 5:48 pm UTC

There's the classic one of using a microwave and grilled cheese to demonstrate the wavelength of a microwave of known frequency, but it's obviously very inaccurate.

by **Xami** » Wed Nov 16, 2011 6:56 pm UTC

When we talk about the age of the universe - are we talking about time as we currently experience it? As if the earth were here from the start?
This is assuming that time is experienced differently based on how fast you are moving right?
Does 'age of the universe' even make sense as a question then?

by **PM 2Ring** » Wed Nov 16, 2011 8:34 pm UTC

Xami wrote:When we talk about the age of the universe - are we talking about time as we currently experience it?

Yes.

Xami wrote:As if the earth were here from the start?

No. The Earth and the solar system are a little over one third of the age of the universe.

Xami wrote:This is assuming that time is experienced differently based on how fast you are moving right?

Yes, according to Special Relativity, time measurements depend on speed, so two observers that are moving relative to one another will disagree on the duration of various time intervals, but that effect is fairly small unless their speed difference is a significant fraction of the speed of light. Also, according to General Relativity, gravity affects time, too, so (for example) time passes more slowly for an observer who is on a planet compared to an observer in free space. FWIW, the GPS system has to take both of these effects into account to give accurate data.

Xami wrote:Does 'age of the universe' even make sense as a question then?

It does. The effects I just mentioned do make things more complicated, but they can be dealt with by specifying the reference frame that you're using to measure the age of the universe in. The most natural frame is that of an observer in free space in the comoving frame of the CMBR. For those of us living in galaxies and on planets the universe will seem a a little younger, because our clocks tick a little slower.

by **Xami** » Thu Nov 17, 2011 2:11 pm UTC

Awesome! Also fwiw, I wasn't asking if earth had always been around, lol, I was extending the first question about our current time experience

by **PM 2Ring** » Thu Nov 17, 2011 5:12 pm UTC

Xami wrote:Awesome! Also fwiw, I wasn't asking if earth had always been around, lol, I was extending the first question about our current time experience

Ah. I get it. And I'm sure you can understand that it's not easy to know what assumptions people may have about the cosmos. We get all sorts of interesting questions here.

by **Aarnoman** » Fri Nov 25, 2011 2:55 am UTC

Well...um...hello everyone *shy*
New to this forum (fora?).

Anyway, to the point, could anybody kindly explain the effects that a black hole has on time? Me and a friend have differing opinions on the effect: Does it distort time? And if so, how does it happen? Is the immense density/gravity enough to do so?

Sorry if this seems like a stupid question, still a stretch away from uni and not a particularly knowledgeable when it comes to Physics. Tried reading up on it on the wiki, but to be honest I ended up being more confused then before...

Thanks in advance.

by **dontpunchme** » Fri Nov 25, 2011 8:18 am UTC

This is probably an elementary question, but:

Is there any direct relationship between the Lorentz contraction and Doppler shifting?

Thanks.

by **Eebster the Great** » Fri Nov 25, 2011 9:26 am UTC

Aarnoman wrote:Well...um...hello everyone *shy*
New to this forum (fora?).

"Fora" is a rarely used plural of "forum."

Anyway, to the point, could anybody kindly explain the effects that a black hole has on time? Me and a friend have differing opinions on the effect: Does it distort time? And if so, how does it happen? Is the immense density/gravity enough to do so?

All massive objects distort both time and space, a result of General Relativity. Black holes are obviously extreme due to their high density. If you get close to a black hole, time dilates, so one second from your perspective will be multiple seconds from a distant observer's perspective. As you approach the event horizon, time dilation increases without bound.

by **dontpunchme** » Fri Nov 25, 2011 9:58 am UTC

dontpunchme wrote:This is probably an elementary question, but:

Is there any direct relationship between the Lorentz contraction and Doppler shifting?

Thanks.

Allow me to rephrase, and pose my question better. Is there any direct mathematical transformation that can prove a relationship between the Lorentz contraction and Doppler shifting? And what does any of this have to do with Maxwell bivectors?

Also, two other questions.

If the light cones from within a black hole's event horizon never intersects an external world line, then how does the gravity within affect the outside world?

One more question: I don't understand the following, quoted from Wikipedia.

Let x, y ∈ M. We say that
x causally precedes y if y − x is future directed null

If a vector subtraction is null/lightlike, why does that imply the above?

by **Aarnoman** » Fri Nov 25, 2011 10:24 am UTC

Eebster the Great wrote:
Aarnoman wrote:Well...um...hello everyone *shy*
New to this forum (fora?).

"Fora" is a rarely used plural of "forum."

Anyway, to the point, could anybody kindly explain the effects that a black hole has on time? Me and a friend have differing opinions on the effect: Does it distort time? And if so, how does it happen? Is the immense density/gravity enough to do so?

All massive objects distort both time and space, a result of General Relativity. Black holes are obviously extreme due to their high density. If you get close to a black hole, time dilates, so one second from your perspective will be multiple seconds from a distant observer's perspective. As you approach the event horizon, time dilation increases without bound.

Thank you very much for clearing that up

by **Eebster the Great** » Fri Nov 25, 2011 8:16 pm UTC

dontpunchme wrote:If the light cones from within a black hole's event horizon never intersects an external world line, then how does the gravity within affect the outside world?

As I understand it, from the frame of an outside observer, the matter is on the event horizon of the black hole, not in the middle in a singularity.

by **dontpunchme** » Fri Nov 25, 2011 10:54 pm UTC

Eebster the Great wrote:
dontpunchme wrote:If the light cones from within a black hole's event horizon never intersects an external world line, then how does the gravity within affect the outside world?

As I understand it, from the frame of an outside observer, the matter is on the event horizon of the black hole, not in the middle in a singularity.

Oh, riiight.

For an external observer, matter never crosses the event horizon and therefore interacts with the world as if infinitely close to the surface.

I'm curious. I know it's impossible to prevent acceleration so close to the black hole, but what happens when a piece of matter is a Planck's length away from the event horizon?

by **thoughtfully** » Sat Nov 26, 2011 12:35 am UTC

dontpunchme wrote:I'm curious. I know it's impossible to prevent acceleration so close to the black hole, but what happens when a piece of matter is a Planck's length away from the event horizon?

Quantum effects near the horizon are imperfectly understood, since a full theory of Quantum Gravity is needed for a complete description. A good book is "Black Hole Wars" by Leonard Susskind. There's also an article in Discover magazine that touches on the topic.

The short answer is that it depends on your motion. If you're an observer at rest with respect to the object, and you're both in free fall, nothing happens. If you're exerting some crazy thrust to keep yourself at rest (which is hard to define if the BH is rotating, like any reasonable BH would), the space around you is going to be around the Plank Temperature, due to Unruh Radiation, which is basically Hawking Radiation reflected through the Equivalence Principle, and you will be rendered into your constituent subatomic particles long before you are able to get there. If you're some other observer not at rest with respect to the test object (other than the familiar distant observer at rest w.r.t. to the BH), I'm not going to try to untangle that mess

by **doogly** » Sat Nov 26, 2011 4:26 pm UTC

You can look up the relativistic doppler effect, that is a result of lorentz transformations.
The classical doppler effect is a different sort of beast, because there is a medium. That's why source receding /= observer approaching for sound, but they are equivalent for light. Similar effects, but not identical.

by **quadmaster** » Mon Nov 28, 2011 2:40 am UTC

What happens if a solid disk is spun so that particles near the diameter are moving at an appreciable fraction of the speed of light? If the outside is looked at as, say, twenty seperate chunks, then each one should decrease in length in the direction of motion, if I understand special relativity. However, if you add up their lengths they should equal the radius times 2 pi, and the radius is perpendicular to the direction of motion, and so does not depend on the motion (again relying on my understanding of relativity)

Can some smart person tell me which of my assumptions is wrong?

by **doogly** » Mon Nov 28, 2011 3:08 am UTC

This is the ehrenfest paradox!
The problem is with 2pi.
...
Seriously. Rotation is a kind of acceleration, so you can't just do vanilla lorentz transforms. You want to look at a metric. It's still flat space (special relativity), no curvature (general relativity), BUT there is an important mixing term --- the metric has a time/angle mixing. So if you look at a constant time slice, a "now," it's not just that this slice depends on the observer (like it does for the more familiar barn and ladder or twin paradoxes) but the now-slice is curved. This happens even when the total space is still flat.

The wiki page for ehrenfest paradox has some more info and some diagrams that may or may not be helpful.

by **Malconstant** » Mon Nov 28, 2011 5:54 pm UTC

The Ehrenfest paradox is just completely ridiculous. I have reasonably serious relativity credentials and I haven't been happy with a resolution for this for a long time now.

I just got done reading the paper cited in the wiki article (O. Gron), which concludes that it is impossible to rotate a born-rigid disc (Edit: that is, you can't take one from rest and then rotate it, or slow one down that is already rotating. It's okay for one to just be rotating though so long as it was created that way), that the proper dimensions of a stationary disc are different from the proper dimensions of a rotating disc. It concludes that an inertial observer passing by the outside of the disc at the same velocity as the point of the disc which it touches will totally disagree with the disc about simultaneity, despite being momentarily at rest with each other. Also, the speed of light itself isn't constant in the rotating frame but rather has directional dependance.

It's just total insanity, basically. When you hear someone talking about a resolution to the Ehrenfest paradox it's a good time to hold onto your wallet. It has a long history of totally contradictory peer-reviewed, published resolutions.

by **Eebster the Great** » Mon Nov 28, 2011 9:19 pm UTC

Malconstant wrote:It's just total insanity, basically. When you hear someone talking about a resolution to the Ehrenfest paradox it's a good time to hold onto your wallet. It has a long history of totally contradictory peer-reviewed, published resolutions.

Just because a whole lot of papers give the wrong answer doesn't mean the right one hasn't been published.

by **doogly** » Mon Nov 28, 2011 9:34 pm UTC

Quite right. Instead, it means something much more like what Malconstant suggested: it's a good time to hold onto your wallet. And be very wary of hand waving heuristics. You have to get out a metric and make love to the crunchy analysis.

by **quadmaster** » Mon Nov 28, 2011 11:41 pm UTC

So, does it take more force to accelerate a rotating disk along it's axis than a non-rotating disk?

by **Yakk** » Tue Nov 29, 2011 1:59 am UTC

Yes, because the rotating disk is heavier.

Yes, because in the limit as the edge of the disk's speed approaches c, a small change of velocity along the axis could result in super-luminal speed: as such, the force required for axis-aligned acceleration must diverge as rotation speed increases.

by **quadmaster** » Tue Nov 29, 2011 2:34 am UTC

Ok, last question: why couldn't a (hypothetically) a reactionless spaceship drive be made by alternately spinning up and stopping two coaxial disks while accelerating them back and forth?

Disks are launched towards front of spaceship ==> disks are spun up during transit to front of spaceship ==> at the front of the spaceship, a force is exerted on the disks by the spaceship to send them back to the back ==> disks are spun down during transit to back of the spaceship ==> a smaller force is exerted on the disks to send them back towards the front of the spaceship

This isn't a practical design, of course, but if it violates conservation of momentum a tiny bit it still violates conservation of momentum.

by **Eebster the Great** » Tue Nov 29, 2011 2:49 am UTC

How are you spinning up and spinning down the disks?

by **thoughtfully** » Tue Nov 29, 2011 4:06 am UTC

quadmaster wrote:This isn't a practical design, of course, but if it violates conservation of momentum a tiny bit it still violates conservation of momentum.

What you have here isn't a practical problem at all. It's a problem in principle. Conservation of Momentum is a pretty important principle, and you can't violate it "a tiny bit".

by **Yakk** » Tue Nov 29, 2011 12:35 pm UTC

Alternative engine: We start with a block of insulated matter at the front of the ship. We heat it up a whole bunch, so its mass goes up. We then push it to the back of the ship.

Next, we cool the matter down, so it is lighter. We then push it towards the front of the ship.

There is a net forward momentum. How does this avoid violating conservation of momentum?

The answer is "the same way your problem did".

by **Tass** » Tue Nov 29, 2011 1:03 pm UTC

thoughtfully wrote:
quadmaster wrote:This isn't a practical design, of course, but if it violates conservation of momentum a tiny bit it still violates conservation of momentum.

What you have here isn't a practical problem at all. It's a problem in principle. Conservation of Momentum is a pretty important principle, and you can't violate it "a tiny bit".

He asks why it couldn't work. He knows it should be impossible in theory, yet his logic finds in only impossible in practice.

The resolution lies in the fact that you'd have to transport energy from one end of the ship to another.

by **quadmaster** » Wed Nov 30, 2011 12:04 am UTC

Eebster the Great wrote:How are you spinning up and spinning down the disks?

I guess a keyed shaft isn't what you are looking for here? I guess some sort of storage device on the main ship, like batteries, and wires to motor/generators that move with the disks?

Oh I think I see. Matter=energy, and so, while this moves energy to the rotors, not matter, it's basically like pushing a sled towards the front of the ship, throwing rocks on to it as it passes the middle, pushing it back towards the back, taking the rocks back off as it passes the midpoint, throwing it towards the front of the ship, rinse and repeat.

Thanks guys!

by **thicknavyrain** » Fri Dec 09, 2011 11:38 pm UTC

If anyone is interested in relativity at it's most basic (time dilation in special relativity) but doesn't have a strong mathematical background, this is for you: http://i.imgur.com/U3DBh.jpg

Made for a friend of mine, probably wouldn't go to waste posted here.

by **Draimey** » Sat Dec 17, 2011 11:08 am UTC

The only change in this didn 't make would come at the expense of brevity is that everything is both a particle and a wave. Protons, electrons, neutrinos, etc. Not only photons.

by **thicknavyrain** » Wed Dec 28, 2011 11:24 pm UTC

This has been messing with my head for a while now. I've tried doing a fora search and some googling but nothing really gives a satisfying answer.

Why in the Minkowski four vector is the spacial/temporal component represented with an imaginary coefficient? I was recently taught that it was always (ct, ir) although wikipedia says it works equally well with (ict, r) (where r is a vector representing x,y,z). That makes sense, but why is either component represented that way? I imagine it's probably something to do with the fact that time only goes in one direction while space goes in both, or maybe something to do with the fact that dimensions are perpendicular and because time is inherently different in nature to the others, its perpendicularity can only be described by the imaginary numbers in reference to the real ones or something strange. I have no clue, it's really bugging me...

by **Eebster the Great** » Thu Dec 29, 2011 4:02 am UTC

In the four vector the zeroth component is not given a factor of i; that is just used for mathematical convenience translating four-vector operations to standard vector operations. For instance, the four vector scalar product <x⁰,x¹,x²,x³>*<y⁰,y¹,y²,y³> is equal to the complex four-dimensional dot product <ix⁰,x¹,x²,x³>*<iy⁰,y¹,y²,y³>. (Note that here x⁰ = ct.)

by **PM 2Ring** » Thu Dec 29, 2011 8:35 am UTC

What Eebster the Great said. We want the geometry of Minkowski spacetime to reflect the invariance of the speed of light, so it needs an appropriate metric signature, i.e., one that gives the Lorentz transformations as the natural symmetry of the space. The use of an imaginary factor on either the temporal component or the spatial components is a mathematical convenience. However, it's also reminds us that a 4-vector pointing in the temporal direction isn't merely orthogonal to the spatial directions in a simple Euclidean sense.

by **Carlington** » Mon Jan 09, 2012 1:52 pm UTC

Not sure if this goes here, but anyway. What is meant when we refer to the global curvature of spacetime? I keep seeing things like "If spacetime has a nonzero positive/negative curvature" and so forth. How do I visualise this, what should I understand it to mean?

by **yurell** » Mon Jan 09, 2012 2:11 pm UTC

I suppose the easiest two dimensional analogues are:

Positive: A sphere
Zero: A plane
Negative: A saddle

Picturing curvature in more than two dimensions is ... really difficult for me, so I just stick with what the maths says.

by **doogly** » Mon Jan 09, 2012 2:16 pm UTC

At this level people are talking cosmologicly, and there, we are gonna assume the universe is homogenous and isotropic. The same for all points (in space, anyway - expanding in time, and if you have drunk enough kool aid at the GR font to get upset by picking out a preferred time direction, we just imagine that all matter that exists in the world can be treated like a single fluid, and it has a rest frame, so that does make things rather special), and the same in all directions.

So, if you are homogeneous and isotropic, there isn't a lot you can vary. You are going to be a space of constant curvature. Positive, negative or zero. Sphere, hyperbola or flat.

Looks like we get flat. Booooooring. Kinda neat though. If you consider how many numbers are positive and how many are negative (infinite) relative to how many are zero (just the one) then it looks like something special is happening. You might start to propose mechanisms that produce flatness, rather than just wanting to call that parameter of the universe something that just so happens to be. Inflation starts to enter your vocab.

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