Watsisname, thank you for the explanation, It's still a complex subject for me. Although I have already read some physics books, I only started to interest myself recently.

If time is relative to any gravitational field the observer is in how do we know the true age of anything closer or further away from us?
(including all objects inside the same field we are in or what ever other gravitational fields it has ever been in)"

Heh.  I've never thought of timing of light as an explanation of stereo vision.  But it does have a grain of sense in it, indirectly.  We have stereo hearing, and though stereo hearing doesn't primarily work that way, it's should be biologically possible to take the timing into account to help locating sound sources.  I wonder if any animals do this (or even humans).  Could this be important for bats, for instance?

Propulsion Disk:  It's okay.  I appreciate that you want to help explain things!   There is some skill for knowing how confident to be in an answer or not, which comes with experience, and yet still is never perfect.  Misconceptions especially can be tough.  We all make mistakes, the best thing is to learn from them!


Aside:  Just for fun, let's compute how far your depth perception works by parallax:

The average distance between a human's eyes is about 63mm (and slightly more for men than women).  The minimum angle that the human eye can resolve is also around 1 arcminute (1/60 of one degree).  

The distance at which the shift in angle due to a 63mm separation of your eyes is 1 arcminute is:

[tex]d = \frac{63mm}{tan(1/60deg)} \approx 220m[/tex]

So beyond a few hundred meters it is impossible to discern distances directly with your eyes using parallax.  You can however gain more distance perspective if you are moving (like driving down a highway) as your motion makes things shift against the background.  Having an intuition for the true size of objects also helps with judging distances, though this is also easier to fool.


If we instead set the angle to 1 arcsecond (1/3600 degree), and the baseline distance to 1AU, then we recover the definition of the parsec used in astronomy, which is about 3.26 light years.  1 parsec is the distance at which the parallax angle for a 1AU shift in perspective is 1 arcsecond.

Thanks Watsisname! But what happened to your mathcode? it was there and then it disappeared.

Do cold temperatures increase when pressure is added to them? Because I held my cold cup and put pressure on it and it got WAY colder!

If time is relative to any gravitational field the observer is in how do we know the true age of anything closer or further away from us?

It is true (and measurable!) that time passes more slowly in a gravitational field.  But for the kinds of fields we typically encounter, this is such a small effect that we can almost always ignore it.  Exceptions are if we need very high precision (e.g. GPS requires such precise time measurements to triangulate your position that it must account for time dilation!), or if we are interested in things very close to black holes or neutron stars.

Let's put some numbers to this, and calculate how much less time has passed at the surface of the Sun (the strongest gravitational field strength anywhere in the solar system) relative to somewhere in deep space where time passes as quickly as it can.  The formula for gravitational time dilation in a spherically symmetric gravitational field is



where t₀ is the time interval in the frame subjected to the gravitational field, t_f is the time interval in a frame "far away" so that the field strength is zero, M is the mass of the object creating the field, r is the distance from its center, and c and G are the speed of light and gravitational constants.

The mass of the Sun is 1.99x10³⁰ kg and its radius is 6.96x10⁸ m.  Given its age of about 4.6 billion years, by how much should we adjust this value to account for the time dilation at its surface?


Answer:  About 9750 years.  Out of 4.6 billion, this changed the answer by just 0.002%!  This is much smaller than the precision by which we know the age of the Sun anyway, so we can ignore it.

For the Earth, gravitational time dilation slows time at the surface by 0.0000000698% (about 7 parts in 10 billion).  That's 3 years out of 4.5 billion years.  Again only important if we need better than 1 part in a billion timing accuracy.

How about at the surface of a neutron star?  Neutron stars weigh slightly more than the Sun, but with only ~10km radius.  Time at their surfaces passes around 70% as fast as time far away!  Now this is getting significant!  This means neutron stars cool a little bit more slowly than you would expect if you didn't treat them relativistically.

To get stronger gravitational time dilation than that, we must get very close to the event horizon of a black hole.  For example, to slow time to 10% the rate of faraway time, we would need to hover at 1.01 event horizon radii (closer than I would ever want to be!)

If we want to also account for the special relativistic time dilation due to orbital velocity, then this changes the answer slightly. For a circular orbit, it changes the factor of 2 in the formula to a 3.

Thanks Watsisname! But what happened to your mathcode? it was there and then it disappeared.

Aye, the math code on the forum sometimes breaks.  Refreshing the page should make it appear again.  I think from now on I'll stick to attaching formulas as images like above.

Do cold temperatures increase when pressure is added to it? Because I held my cold cup and put pressure on it and it got WAY colder!

For a cold cup I don't think so.  You can cool a hot cup to room temperature more quickly by pressing your hands on it, but this is not because of pressure but rather because you help conduct heat from the cup to your hand, which is faster than it would cool just by radiating.  I use this technique to help cool my coffee.

Heh.  I've never thought of timing of light as an explanation of stereo vision.  But it does have a grain of sense in it, indirectly.  We have stereo hearing, and though stereo hearing doesn't primarily work that way, it's should be biologically possible to take the timing into account to help locating sound sources.  I wonder if any animals do this (or even humans).  Could this be important for bats, for instance?

Yeah, I was thinking about this also. It turns out that bats use it as you said for echolocation. Sound waves, as electromagnetic waves, have no internal clock-like property that could carry the information of how old the wave is (as explained by Watsisname), but bats know when the sound wave was created since they were the source of it and can measure the time delay between the emmision and reception after the echo returns (sound bouncing over some solid surface in the surroundings). By measuring those time delays they can measure distance in the same way a sonar works. In the article on echolocation of Wikipedia it is stated that:

In the Inferior colliculus, a structure in the bat's midbrain, information from lower in the auditory processing pathway is integrated and sent on to the auditory cortex. As George Pollak and others showed in a series of papers in 1977, the interneurons in this region have a very high level of sensitivity to time differences, since the time delay between a call and the returning echo tells the bat its distance from the target object. While most neurons respond more quickly to stronger stimuli, collicular neurons maintain their timing accuracy even as signal intensity changes

I've tried to find some quick data on how accurate are bat's biological clocks. In this paper they talk about 4 ms (milisecond) time delays that can be noticed by bats (I didn't pay a lot of attention to the read so maybe I'm wrong). If sound travels at 345 m/s then an object 1 meter away would imply a time delay of (2 m) / (345 m/s) = 0,0058 s = 5,8 ms. Suppose they have an accuracy of 2 ms in their internal clocks. Then bats would estimate the time delay to be between 5,6 ms and 6,0 ms, meaning that they would estimate that the object is between 96,6 cm and 103,5 cm away from them. Knowing that there's an object 1 meter away with a 3,5 cm uncertainty is amazing to me. Obviously our visual system is way better for that; I can press with my fingers a milimeter sized object a meter away from my eyes without having to try more than once (even If I need to do that slowly). But still cm accuracy using sound is crazy. And crazier still is the fact that bat brains are able to measure millisecond time steps, I can't even pause my cronometer in a specific tenth of a second of my choice even if I try many times.
Also there's a problem with this system. If the sound emmited by the bat has too a large duration then the echo could overlap with the sound still been emmited and the bat could get confused. This is the reason bats emmit short pulses if necessary. Their sound pulses can range from 100 ms to 0,2 ms in duration (that's crazy short). For closer objects the 0,2 ms pulse is great since there is no time for the echo to return and overlap with the emmision but the problem is that with such short pulses the ammount of information that comes back could be very scarce. So bats tune the pulse durations and timings at different ranges to see with different accuracy things at different distances. In Wikipiedia is stated that:

A single echolocation call can last anywhere from 0.2 to 100 milliseconds in duration, depending on the stage of prey-catching behavior that the bat is engaged in. For example, the duration of a call usually decreases when the bat is in the final stages of prey capture – this enables the bat to call more rapidly without overlap of call and echo. Reducing duration comes at the cost of having less total sound available for reflecting off objects and being heard by the bat.

The time interval between subsequent echolocation calls (or pulses) determines two aspects of a bat's perception. First, it establishes how quickly the bat's auditory scene information is updated. For example, bats increase the repetition rate of their calls (that is, decrease the pulse interval) as they home in on a target. This allows the bat to get new information regarding the target's location at a faster rate when it needs it most. Secondly, the pulse interval determines the maximum range that bats can detect objects. This is because bats can only keep track of the echoes from one call at a time; as soon as they make another call they stop listening for echoes from the previously made call. For example, a pulse interval of 100 ms (typical of a bat searching for insects) allows sound to travel in air roughly 34 meters so a bat can only detect objects as far away as 17 meters (the sound has to travel out and back). With a pulse interval of 5 ms (typical of a bat in the final moments of a capture attempt), the bat can only detect objects up to 85 cm away. Therefore, the bat constantly has to make a choice between getting new information updated quickly and detecting objects far away.

They gain even more accuracy by analyzing the interference patterns between the emmited and reflected sound waves. That allows them to gain accuracy levels in the same order of magnitude of the wavelength of the sound used. That's the reason that led bats to use high frequency for their echolocation system (high frequency is shorter wavelengths). 

Microbat range in frequency from 14,000 to well over 100,000 Hz, mostly beyond the range of the human ear (typical human hearing range is considered to be from 20 Hz to 20,000 Hz). Bats may estimate the elevation of targets by interpreting the interference patterns caused by the echoes reflecting from the tragus, a flap of skin in the external ear.

A frequency of 100.000 Hz in sound waves means wavelengths of 0,3 cm. That is trully an impressive system.
This can also work for light! Electromagnetic waves don't carry a clock on them and don't age (part of the reason is that at the speed of light no clock ticks and the rest of the reason is that there's no property in waves to inprint the information about the time of their creation on them, nor wavelength, nor intensity nor polarisation can tell you that infromation). So we would need to know when the light was emmited to measure the difference in time until arrival to our eyes. We could do that like bats; been us the ones that emmited the light and expecting it to bounce somewhere so it returns to our eyes. That way we would have complete knowledge of the time of emmision and the time of arrival. But this is problematic; first producing sound waves is easy but light not so much, neither humans nor bats have bioluminescence. Second, we need light to not disperse too much with distance since we could end not seeing the reflected light (the echo) when it comes back, so we need... a laser (no living thing have laser bioluminiscence as you might immagine, beside space lazer electric sharks). Third, we need to tune our laser so that it bounces correctly in a large diversity of surfaces (we don't wan't to be able to locate only clean mirrors around us right?), this is easier for sound since sound bounces nicely for many surfaces (even if some are able to absorb sound) but for light this is a mess. We would also confuse a transparent window with a black coat (visible light would be absorbed) with a void since no light would return in all three cases for different reasons. We might overcome this by tunning the frequency of our laser at will (the transparent window could reflect in some other part of the electromagnetic spectrum), but we would probably need a lot of tunning to see the pletora of textures light interacts with. Fourth, if something emmits light it could confuse us and make our visual system go crazy (as high frequency sounds confuse bats), we sould use our laser visual system in a dark cave or something like that to have clear sight, the sun, the light reflected by each object could potentially make us belief in wrong time-delays of our light pulses and change entirely the 3D scenario as we perceive it. Even in dark conditions if our laser needed to be tunned in the infrared we would have a lot of objects emmiting and confusing our sense of laser-echolocation. Fifth, and this is the biggest problem of all, we would need our biological clocks to be in the 0.03 nanosecond accuracy level (if we wanted at least cm accuracy). Thus we would also need an atomic clock inside our body to tell us at least some accurate distances. Sixth, for our brain and nervous system to be able to process those fast signals in real time we would need electric-circuit-like speed, but chemical transport of information between neurons goes way slower. The fastest clock you can find in humans relies in a chemical process that has a timestep of 100 ms at best (that is 3 billion times slower than the timestep we are asking for here).
So! For the depth perception mentioned by PropulsionDisk we just need laser eyes with tunning capabilities and a biological atomic clock inside an extremely fast computer-like brain. But you know what? Even if we natural selection hasn't allowed us to be like that we are clever little monkeys and we can build a laser, an atomic clock and a computer. And in fact we have built this "sensory system" here on Earth and used it in space to gain depth perception, breaking the barriers imposed by evolution on us!

[center][/center]
Meet the laser ranging. We send pulses of light from an observatory with a laser to the Moon and wait for the reflection (using the same observatory to capture the dim light). An atomic clock counts nanosecond ticks until the pulse returns to Earth after a 720.000 km voyage of just two seconds. Here a computer uses the information of several of those pulses to gain more and more statistical confidence on the time-delay of the signal. With this we, clever little monkeys, have been able to see like bats inside the cosmic cave the Earth-Moon system is, and we have a depth perception that allows a distance measurement to the Moon of submillimiter accuracy (yes, you heard that correctly).
We have sent "robotic bats" to the Moon and Mars to use their laser-atomic-ecolocation system to gain depth perception there and bring us the most accurate topographic maps we have of both worlds. Also radar works the same but with radio waves. With radar we have been able to see other planets and nearby minor bodies from the surface of Earth.
Here you have a bat image of the surface of the Moon by LRO (compiled not by a bat brain but by the computer program of Sean Doran, a fellow SpaceEngine forum member):
[youtube]D2yAdKzWS0k[/youtube]
Radar is exactly the same but using radio waves. With raday we can see Venus in depth and nearby minor bodies from the surface of Earth! Here you have a bat vision of the asteroid 2014 HQ124 made by the "Arecibo bat":

As Watsisname said that would also make easier to have depth perception for objects separeted by large distances and instead of that we have more difficulty to perceive the distance between two mountains than between two persons nearby. Parallax is our main source of depth perception and is usually called stereoscopic vision. If we had "laser ranging depth perception" as PropulsionDisk suggested then closing one of our eyes would have no impact in that ability, but since we use stereoscopic vision we need two eyes at least, to triangulate.

Man, I love those grainy asteroid pics. Here is a question (actually three disguised as one) that probably has an easy answer or a long answer (I'm interested in the long answer):

I remember reading in Carl Sagan's [i]Cosmos[/i] about FTL technology and what year AD we may discover it, based on plotting out the technological advances we've made in transportation (examples given was the invention of the wheel, steam, automobiles etc) sequentially as they happened, with FTL being presented as the next great leap, predicted to occur at either three times in the future, some time in 22nd century, the 25th century or never at all. Presented with this data, together with considering that even if the Rare Earth hypothesis' and Great Filter hypothesis are true (we may not know mathematically within the Drake equation until we actually find life beyond Earth - but lets use the modern number that there are a few thousand civilizations in our galaxy), when do you (the people of this forum) think we may discover sometime in our future, without ANY shadow of doubt (quod erat demonstrandum):

- An alien civilization more technologically advanced then us somewhere in the Milky Way galaxy, light-lag permitting and barring non-technological life being found.

-FTL travel being possible or completely impossible.

How might the discovery of one, affect the other in non-obvious ways (ex. NOT "the aliens know about FTL, and give us the tech")? I was thinking that though the mathematics behind physics are standard throughout the observable universe, it is philosophically possible that our concept of numbers is subjectively species-bound (and perhaps then self-crippling in our viewing of the universe?), and thus might an alien civilization race develop some parallel to our Math that their brains find objective proofs for in the observable universe, that allows for mass to transport faster then light without infinite energy?

PS I am aware of the various arguments for/against FTL technology in general. These questions are more technocratic/cosmological in nature.

- An alien civilization more technologically advanced then us somewhere in the Milky Way galaxy, light-lag permitting and barring non-technological life being found.-FTL travel being possible or completely impossible.How might the discovery of one, affect the other in non-obvious ways (ex. NOT "the aliens know about FTL, and give us the tech")? I was thinking that though the mathematics behind physics are standard throughout the observable universe, it is philosophically possible that our concept of numbers is subjectively species-bound (and perhaps then self-crippling in our viewing of the universe?), and thus might an alien civilization race develop some parallel to our Math that their brains find objective proofs for in the observable universe, that allows for mass to transport faster then light without infinite energy?

Very interesting question(s) Stellarator! and for your questions my answers are NO, YES, and YES, Skiping the first one for the reason I state at the end, I would say that FTL technology is possible it's just not discovered yet by anything in this galaxy, and the last one is linked very tightly to the first one, but I say that aliens are "subjectively species bound" as nothing would make any sense on they're worlds and would never be logically correct, sorry I couldn't get in depth with all that,  it's just that all of those are linked to personal belief.

I was thinking that though the mathematics behind physics are standard throughout the observable universe, it is philosophically possible that our concept of numbers is subjectively species-bound (and perhaps then self-crippling in our viewing of the universe?), and thus might an alien civilization race develop some parallel to our Math that their brains find objective proofs for in the observable universe, that allows for mass to transport faster then light without infinite energy?

I don't believe so.  Math may certainly be expressed differently, but when used as a tool for describing nature, then it must be consistent with nature.  An alien civilization's formulas of physics might look very different from ours, but they must make the same predictions for the same phenomenon.  All observations that we have are consistent with relativity's predictions.  Massive particles can only approach the speed of light -- never reach or exceed it.  Even if you are in a spaceship undergoing constant acceleration, it will never reach the speed of light.  If this was incorrect then we would have already easily exceeded the speed of light in particle accelerators.

Many speculate that it may be possible to exceed the speed of light by some distortion of space-time, like the Alcubierre drive or something similar.  The math can be expressed that way, but again there are deep underlying principles of physics that suggest it should not be possible.  It introduces causal paradoxes, for example.  

Ultimately, if faster-than-light travel is possible, then it must work in some very bizarre way which is outside the current scope of relativity.  It would be truly marvelous if it is ever figured out.  But again, so far all observations are consistent with relativity, and these observations have been made in a very wide range of scales and conditions -- even up to black holes colliding.

I agree with the sentiments presented here in answer with my questions, thank you for sharing your thoughts on the matter. I'm glad I can share these musings with you and get a fairly educated opinion - most of the time when I try to engage the people I know (in real life or in the cyberspace) with theoretical physics I get closed-minded or completely vapid retorts since not many people like to ponder these things in intimate detail unless they share a passion. In regards to FTL, it certainly helps to have a intuitive grasp of mathematics and physics and a general love for learning something new, nowadays a thing people kill with sensationalism. I try not to state this as an elitist sentiment. I find the geometry of time causality and its relationship with the Lorentz Transformations of fields to be endlessly fascinating, the way they unite the observers with the universe at large with synchronous events that are the speed limit at which data can be relayed. Faster-Then-Light, is actually a misnomer! It is the SPEED OF CAUSALITY WITHIN SPACE/TIME. If c=infinity, the universe would be without mass or matter, and the very universe would cease to exist!

I imagine a lot of people on this forum are probably familiar with what I am babbling about, but to those to whom this all seems arcane, I always found the Minkowski Space/Time Diagram to be useful,



together with this short video:

[youtube]HUMGc8hEkpc[/youtube]
I found it simplified[i[ things.

On a side note, I found this in my daily diet of science news a while back:
https://io9.gizmodo.com/5963263/how-nasa-will-build-its-very-first-warp-drive

It might just be NASA sensationalism, but it is sure intriguing. I wonder how they will get around the massive bang of gamma radiation Alcubierre warp-drives let off when operating - something that can be detected from across the galaxy and indeed vindicates the belief that such a technology has never been used in the Milky Way (maybe the aliens shielded themselves somehow - but as I understand it shielding from gamma radiation is hard)?

What do people here think about string theory?  Is it a strong candidate for a unified theory, or is it the wrong path?

Maybe it has some beauty in unifying gravity and the quantum world, but there is one thing about its popularity that I don't get: 11 dimensions?  (or 10 or 26, whatever)  That makes the universe so mindblowingly large that these extra dimensions ought to serve other purposes than just unify some equations.  It should make tons of predictions, but, as far as I understand, it doesn't.

I'm a programmer, and my concerns are easily expressed by a programming analogy.  Let's say I have a program using a 4-dimensional array.  The only trouble with it is that it's a bit awkward to index.  I have to use non-linear functions and scattered if-then-else to do it, so it's not pretty or efficient to compute, but it works pretty well nevertheless.

Then some punk approaches me and says that he have solved the indexing problem.  He's changed my program so the index is a single expression free from special cases and such.  He also says that he had to make the array 11-dimensional to make it work.

I would yell at him: YOU GOT TO BE KIDDING!  Let's say that I had a modest array, 32 bytes for each dimension, so its total size was 32⁴ bytes = 1 megabyte.  Now the array is 32¹¹ bytes = 32 petabytes.  And the extra bytes serve no other purpose than to simplify the index computation.  99.999999997% of the array is empty, but my program is shorter.  I would immediately revert his change and ask him not to break my program again.

If my original program used to do some basic physical simulations, and, as a bonus, out of the new 11-dimensional array popped out solutions for cold fusion, anti-gravity, and a cure for cancer, then the change would be worthwhile.  I could possible settle for less as well, but it would have to offer some other benefits of significance.

I'm not a physicist, and I can not say much about string theory. (I could, but it probably would not be very scientific, and above all, I can not do it in English.)
But that we need more than four dimensions to create the unified field theory, I think is very likely.
(Perhaps there are not 11 dimensions. Maybe there are more. )

I haven't studied string theory in any real detail either.  The greatest exposure I've had to it so far was watching a couple of students work out some equations with it on a board while I occasionally asked questions and otherwise worked on something else entirely.  

At any rate, from my non-expert viewpoint I mostly agree with you, midtskogen.  Without seeing any clear predictive utility for it yet, it seems like more of a shot in the dark, guided by a desire for mathematical elegance and a need for self consistency.  I look at it and go "this is a neat theoretical exercise, but how do we know it's the right path?"  I don't think we do.  Sometimes great scientific advancements come from the theoretical side, but more often it is a balance between theorizing and experimentation.  I think string theory falls too far behind on experimental support. 

However, I don't think that the apparently useless complexity or scale added by string theory makes it less likely to be right.  Relativity didn't add any dimensions, but it did mix them in this weird non-Euclidean way, which at a first glance could make someone go "why on Earth would nature work that way?".  Worse yet is particle physics which just gets even more exotic the further down we go (or more energy we apply).  There is a famous quote by one of the physicists, who upon seeing the properties of the newly discovered Muon, said "Who ordered that?"  

So I don't have any real attachment to string theory and honestly wouldn't really call it a theory yet in the strictest scientific sense.  If I did study it rigorously my opinion might change, but for now I think "Who knows if it's right... I just hope it ends up producing something testable."

Well, it's more a question about simplicity than an exact description of reality which is not independently verifiable.  We can't compute the likelihood.  Occam's razor doesn't have a proof.  The question becomes whether assuming all these extra dimensions is any better than living with the non-unified theories.  But, yes, the simplicity of the new sometimes grows with the time of familiarisation.  Relativity caught on pretty quickly, I think.

It's not strictly necessary to make predictions of new things to be "right", as long as there is falsiability.  What if there are no more elementary particles to be discovered?  That shouldn't disqualify us from making new theories which can describe them all.  But if adding new dimensions is what it takes to be "right", it begins to smell like epicycles all over again.  Epicycles are also "right" if you keep adding enough of them, but it's fair to worry that a path that becomes more and more exotic goes nowhere.

Maybe there is a mathematical proof that any set of elementary particles can be described if you add a sufficient amount of dimensions. Then we're on the wrong path.