Gravity center; Virtual particles near BH; Motion reality; Universe contracting

[Boy@n]

I’ve got few simple questions (and views) about which I’m pondering on for some time now and since I’m layman on these topics I’d love to hear thoughts and insights about them from some of the great contributors at this forum. Thank you!


-- Is gravity in center of star highest, lowest or something in between? Imagine being put in center of a star, would you be smashed - by gravity pressing on you from all sides? Or being torn apart - by gravity pulling you apart from all sides? Or perhaps your body would feel no gravity effect at all - gravity from all sides canceling itself out?


-- Imagine a pair of virtual particles popping into existence near Black Hole horizon, where BH might immediately suck one particle in and leave the other one out to stay - wouldn't this increase total mass of Universe? And thus brake conservation of energy law?


-- How is movement, actually any motion, possible? (Strange question indeed, but please bare with me.) Imagine moving your hand from point A to point B, now, how many 'distinct steps' happened in that movement? Watching that on TV in slow motion would reveal 25 or 30 fps (frames per second), recording that motion with newest slow-mo cameras would reveal thousands of fps... the better the slow-mo camera we develop the higher number of fps will be recorded. But the question is, how many fps happened for real? It cannot be infinite number of fps or else we could never move from point A to B, since it would mean making infinite finite, right? (From this POV the initial question.) Could we calculate all steps (fps) by dividing that distance with Plank length (10^-33 cm)? But then again, isn't it puzzling that a single hand movement made such enormous number of distinct steps (say 10^32 fps) in such energy efficient way, which no camera could ever record fully?


-- Is Universe really expanding or is everything in it conctracting? Would not we observe the same things in both cases (red shift and all objects moving appart)? The idea for contracting comes to me due imposibility for existence arising out of pure nothingness (which is not void of just all matter and energy, but even space-time and quantum fluctuations, and stuff like awareness or whatever imaginable or not). So, since existence (of something, whatever the true nature of its essence is) must be eternal, then another way to explain our observable Universe is to imagine that before birth of our Universe there was (is) a complete solidness of somethingness infinite, which then exploded not from a singular point but from everywhere. Imagine a glass of water, and let's say water is that complete solidness, all molecules being perfectly connected, now imagine this water exploding in sense that all water molecules go appart, this gives birth to billions of tiny water drops and so volume of glass which contained all water is now highly increased, and that which now separates all drops is now empty space (nothingness), now, if these drops would all stay in its place and become shrinking it would look like if empy space in between of them is expanding. How to know which model (expanding, contracting) is true? IMO Universe is expanding, but I'd say it came into existence (the way it is) from complete solidness 'exploding everywhere' (at Plank's length more exactly).

 

[granpa]

https://www.physicsforums.com/showthread.php?t=82309&page=6

 

[granpa]

isn't it puzzling that a single hand movement made such enormous number of distinct steps (say 10^32 fps) in such energy efficient way

why is that surprising? look at how simulations are run on computers.

 

[Boy@n]

why is that surprising? look at how simulations are run on computers.

Computer simulations don't generate as many frames per second as reality does, far from it, they generate only as much as it's needed for human eyes to think movements are smooth (60 fps or so). In fact, computers will never be able to generate that much frames as in reality.

 

[granpa]

thats not at all true. they generate as many frames as they need to to run the simulation accurately. Simulations of the orbits of the planets over billions of years must be done in small steps or they would quickly become inaccurate.

yes they will never be able to match reality

 

[Boy@n]

https://www.physicsforums.com/showthread.php?t=82309&page=6

Thanks for providing that link - I've read whole tread and if I got it right there are two main forces to be considered, gravitiy, which would be zero at the center, and pressure, which would be maximal at the center, correct?

 

[Boy@n]

they generate as many frames as they need to to run the simulation accurately

Understood, but that's still way less than number of FPS of real world.

 

[granpa]

Thanks for providing that link - I've read whole tread and if I got it right there are two main forces to be considered, gravitiy, which would be zero at the center, and pressure, which would be maximal at the center, correct?

yes you are right

 

[Chalnoth]

There is no "FPS" of the real world, however. There can't be, because that would violate relativity. Basically, if time is separated into slices, then those slices would look very different to an observer moving at high velocity with respect to us, which would mean there would be a preferred reference frame.

There is a way to quantize space-time without violating relativity, but it requires a random distribution of space-time points.

At any rate, it doesn't actually matter in the end if space-time is separated into discrete steps or not, because once the steps are small enough compared to the motion, the motion might as well be perfectly continuous.

 

[Boy@n]

...the motion might as well be perfectly continuous.

Thanks for your insight. If I understand you properly, would 'perfectly continuous' motion mean that, if we'd like to record them all with perfect camera, that we'd have to record infinite number of 'slices'?

Well, that's exactly why it looks inredible to me that motion is even possible. More clearly put, the two reasons being: first, 'perfectly continuos' motion means we'd have slices shorter than Plank's length (is that possible?), second, it means doing something infinite with finite time (which seems also impossible).

And if motion isn't 'perfectly continuos' then the question is, what determinates limit of discrete steps/slices/FPS and how many are there?

Whatever the case, the fact that moving is natural to us, and for most people the question never even occured, still amazes me.

An apparently simple and most basic thing in our life, yet, without decisive answer. Am I the only one being puzzled by this?

 

[Boy@n]

yes you are right

Still, this doesn't look (logically) right to me.

If gravitiy is zero at the center of a star (or planet), then pressure at the center should be zero too, not maximal...

Well, if maximal gravity within a star is about in the middle of surface and center (and this goes all-around), thus mass of material composing that star is being pulled toward that point, thus releasing preassure in center... No?

 

[granpa]

pressure at a given point is equal to the weight of material above that point. why would the weight of material above that point be zero

the net gravity is always pointing down

look up gravity of a spherical shell. you should get lots of hits.

 

[Chalnoth]

Thanks for your insight. If I understand you properly, would 'perfectly continuous' motion mean that, if we'd like to record them all with perfect camera, that we'd have to record infinite number of 'slices'?

I think you're running afoul of Zeno's paradox here. When talking about fundamental physics, the natural amount of time it takes to cross a Planck length is the Planck time. But something that takes a Planck time to cross a Planck length travels at the speed of light, so things like ourselves are actually moving incredibly slowly by comparison.

Well, that's exactly why it looks inredible to me that motion is even possible. More clearly put, the two reasons being: first, 'perfectly continuos' motion means we'd have slices shorter than Plank's length (is that possible?), second, it means doing something infinite with finite time (which seems also impossible).

Zeno's paradox is a paradox only because of using an incorrect numbering system for the problem at hand. If we, for the moment, imagine that space-time is perfectly continuous, then any division of space-time is an artificial division. If we consider motion across one meter that takes one second, then whenever we artificially divide this motion into steps, we not only are looking at a smaller interval of time, but also a smaller interval of space. It takes no more time to travel one meter in one second than it does to, for example, travel five 20cm steps each in 0.2 seconds.

When we attempt to consider the case where we've artificially divided the system into an infinite number of steps, mathematically we're dividing by zero, so it's no surprise that we get nonsense out. The answer is to just not divide by zero.

This all just goes back to Galileo, who proposed that it is impossible to determine whether you are moving or not (that is, that all reference frames which more uniformly are equivalent). The implication of Galilean relativity is that there can be no mystery as to how things move, because moving is, as far as fundamental physics is concerned, the same as staying still. If the underlying space-time is perfectly continuous, this works out very well. If, on the other hand, the underlying space-time is discretized (separated into steps), then there are potential issues that arise. But in any case motion isn't difficult at all.

 

[Boy@n]

But in any case motion isn't difficult at all.

You mean understanding motion properly isn't difficult? (It's obvious from daily experience that motion isn't difficult in real life.)

Well, even in your explanation you used "if", if space-time is perfectly continuous or if space-time is discretized... I guess that this means that science is not sure about this yet, so, how can we say understanding motion is simple if we don't even know the truth of space-time being continuous or not?

And if space-time is indeed continuous, why cannot we make a camera which would record reallity as it is? In the end cameras are made of same stuff as that which it records, atoms and quarks, so, it should be possible to record motion in a continuous way, but why does it look to me that this won't ever be possible?

P.S. I very much appreciate your replies, hope it doesn't look as if I am not accepting your explanations -- I'd just like to understand it all better.

 

[Chalnoth]

You mean understanding motion properly isn't difficult? (It's obvious from daily experience that motion isn't difficult in real life.)

Well, there is always the possibility of interesting subtleties that are difficult to understand. I'm just saying that a perspective that leads to nonsense (motion can't happen) obviously gets something wrong somewhere. In the case of Zeno's paradox, it's that by dividing up space in that way, you end up dividing by zero.

Well, even in your explanation you used "if", if space-time is perfectly continuous or if space-time is discretized... I guess that this means that science is not sure about this yet, so, how can we say understanding motion is simple if we don't even know the truth of space-time being continuous or not?

The basic answer is that all of our experiments are consistent with a perfectly-continuous space-time. So if space-time is discretized, it must be discretized in such a way that it doesn't make a difference for any of our experiments to date.

And if space-time is indeed continuous, why cannot we make a camera which would record reallity as it is? In the end cameras are made of same stuff as that which it records, atoms and quarks, so, it should be possible to record motion in a continuous way, but why does it look to me that this won't ever be possible?

Rather it's because in the end, cameras make use of photons to produce an image. The maximal sensitivity you can possibly have is a camera which records each individual photon as it comes in, which means you have to wait a little while to collect enough photons to produce an image. This means that whenever you take a snapshot, you are actually taking an image of the light coming from that object summed up over some finite span of time. Decrease the span of time too much, and you just won't get a sensible image out, because not enough photons will have struck your camera.

 

[Boy@n]

pressure at a given point is equal to the weight of material above that point

I don't understand this well, every point on surface could be seen as having pressure of all the weight of material above it, if you chose a correct viewpoint... By what you are telling me I visualize this (which doesn't seem right): imagine standing on top of Earth, then the bottom part would bear all the weight, including yours, but if you move down and stand at the bottom of Earth surface you are not feeling the pressure of all the weight above you, you feel no pressure at all, except your own, due to gravity.

why would the weight of material above that point be zero

Say you are standing still in center of Earth, you feel no gravity effect, but you say you feel pressure of weight of whole Earth all around you, but now imagine splitting Earth in half while you still stay in same position, now, you'd still feel no gravity, since half of Earth is on your left side and the other half on your right side, but, in this case, you'd also not feel any pressure at all, right? Why it is different if you unite the two halves back?

look up gravity of a spherical shell. you should get lots of hits.

Looking... http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.html and http://en.wikipedia.org/wiki/Shell_theorem ...lots of math tho...

 

[Chalnoth]

pressure at a given point is equal to the weight of material above that point. why would the weight of material above that point be zero

Oops, I forgot that I was going to respond to this. It turns out that this isn't actually true. It sounds perfectly reasonable, but it doesn't work this way in detail. Basically, it all comes down to the fact that pressure acts like a scalar, not a vector.

The way this is done in reality is to take a fluid and consider dividing it into discrete chunks. Then apply Newton's laws to each individual chunk of fluid with respect to its neighbors. Then take the limit as the size of the chunks goes to zero, and you end up with the Navier-Stokes equations. It turns out to be a bit complicated in detail, unfortunately.

 

[Boy@n]

Well, there is always the possibility of interesting subtleties that are difficult to understand. I'm just saying that a perspective that leads to nonsense (motion can't happen) obviously gets something wrong somewhere. In the case of Zeno's paradox, it's that by dividing up space in that way, you end up dividing by zero.

The basic answer is that all of our experiments are consistent with a perfectly-continuous space-time. So if space-time is discretized, it must be discretized in such a way that it doesn't make a difference for any of our experiments to date.

The nature of "perfectly-continuous space-time" still puzzles me. I cannot imagine what that really means considering that in science we can quantitize everything, or not? If not, if existence (not just space-time) is perfectly-continuous, there might be no "fundamental particle(s)", right?

Also, there is a theory arguing that our world is a computer simulation... but aren't experiments which are showing a perfectly-continuous space-time proving that our reality cannot be a computer simulation? (Since, it looks impossible for a computer simulation to generate infinite numbers of FPS, so that motion appears the same as observed in our nature. No processing power could ever be enough to do it.)

Rather it's because in the end, cameras make use of photons to produce an image. The maximal sensitivity you can possibly have is a camera which records each individual photon as it comes in, which means you have to wait a little while to collect enough photons to produce an image. This means that whenever you take a snapshot, you are actually taking an image of the light coming from that object summed up over some finite span of time. Decrease the span of time too much, and you just won't get a sensible image out, because not enough photons will have struck your camera.

I see. So, what would be the shortest time to get enough photons for generating a sensible image with current technology, if you might know? Actually, I am asking how many frames per second is possible to capture using best current technology.

What about theoretical limit, how many FPS could be captured? For example, we are recoding a high-speed bullet flight, is it (not enough) photons being reflected from that bullet, which are being recorded, which set the upper theoretical limit of how many FPS we could record? Which is?Hmmm, just occurred to me, if photons (which are particles/waves) would have to reflect back whole (every 'step') of the motion (which is said to be continuous) then there would have to be infinite amount of them to cover whole motion?!

So, either photons cannot reflect back reality in all its fullness, or reality is not continuous?

I probably got it all wrong?

 

[Chalnoth]

The nature of "perfectly-continuous space-time" still puzzles me. I cannot imagine what that really means considering that in science we can quantitize everything, or not? If not, if existence (not just space-time) is perfectly-continuous, there might be no "fundamental particle(s)", right?

Continuity is just a statement that "position" and "time" are real numbers. If you want to divide space-time up into discrete steps, then things get considerably more complicated.

But all of quantum mechanics today, as well as General Relativity, consider space-time to be continuous in this manner. The division of space-time into discrete steps is potentially a feature of quantum gravity, but we don't yet know that for certain.

Also, there is a theory arguing that our world is a computer simulation... but aren't experiments which are showing a perfectly-continuous space-time proving that our reality cannot be a computer simulation? (Since, it looks impossible for a computer simulation to generate infinite numbers of FPS, so that motion appears the same as observed in our nature. No processing power could ever be enough to do it.)

Our universe as a computer simulation is at best baseless speculation. If it turns out that certain aspects of the behavior of our universe are incomputable (which is a possibility), then this is fundamentally impossible.

But I'd just like to point out that one rather general feature of computer simulations appears to be the application of approximations: when running a computer simulation, you typically aren't interested in getting all of the details correct, you're just interested in getting the answer to a specific question. And answering a specific question can usually be done by using approximations to the true behavior. If our universe were a simulation, then, we'd expect to see approximations that "break" the laws of physics. Instead we see a universe which is vastly, vastly more detailed than it needs to be to get most any observable we might think of.

Another way of looking at it is that in a simulation, you expect things like the laws of thermodynamics to be programmed-in, instead of allowing those laws to arise as a consequence of the microscopic behavior of the program. The reason is that it takes vastly less work to program in these laws than it does to simulate the underlying behavior that replicates them. But in our universe the laws of thermodynamics are a consequence of underlying behavior (as well as many other laws/theories). So, at least on the surface, our universe certainly doesn't look like any computer simulation we would ever run. We can't say for sure that it isn't, but there's definitely no reason whatsoever to believe our universe is a computer simulation.

I see. So, what would be the shortest time to get enough photons for generating a sensible image with current technology, if you might know? Actually, I am asking how many frames per second is possible to capture using best current technology.

That really depends on the situation. It depends upon how high-resolution you want your image to be. It depends upon how low you want the noise to be. It depends upon how bright your source is. And it depends upon the collecting area of your camera.

One might be able to consider a theoretical upper limit for a massively-bright source on a camera with a very large collecting area, in which case the minimum time required would be the minimum time to absorb some minimal number of photons, which would be a couple orders of magnitude more time than the period of a single photon. So if you have a bright enough source, perhaps somewhere in the $10^{-12}$ second range for visible light? I don't think you'll get even remotely close to this limit for any realistic scenario, as this would require a tremendously bright light source.

Bear in mind that the Planck time is ~$10^{-44}$ seconds.

Hmmm, just occurred to me, if photons (which are particles/waves) would have to reflect back whole (every 'step') of the motion (which is said to be continuous) then there would have to be infinite amount of them to cover whole motion?!

The resolution of a single visible photon to motion is on the order of about $10^{-15}$ seconds (this is the time period for one oscillation of the photon wave). Movements shorter in time than this just won't impact the behavior of the photon much.

 

[Boy@n]

Chalnoth, thank you for all your explanations!

Interesting to note that the Plank time is ~10^-44 seconds and that the resolution of a single visible photon to motion is on the order of ~10^-15 seconds...

So, now, if we consider that any movement consists of at least as many steps as number of Plank's length fitting them (each step being finished in Plank's time), then this also means that we can never 'see' motion (via light/photons) as it really happens in reality (not in present, nor in past via reviewing recorded images).

All this makes me just ponder more on true nature of reality.

 

[Chalnoth]

Chalnoth, thank you for all your explanations!

Interesting to note that the Plank time is ~10^-44 seconds and that the resolution of a single visible photon to motion is on the order of ~10^-15 seconds...

So, now, if we consider that any movement consists of at least as many steps as number of Plank's length fitting them (each step being finished in Plank's time), then this also means that we can never 'see' motion (via light/photons) as it really happens in reality (not in present, nor in past via reviewing recorded images).

All this makes me just ponder more on true nature of reality.

Just means we have to use shorter-wavelength/higher-frequency light to do so. This is why we build big particle accelerators like the LHC: high energy = shorter wavelength. I'm not sure we'll ever have the engineering capacity to get down to the GUT scale, though, let alone the Planck scale.

 

[Boy@n]

Putting the above realization in a real life example tells us something fascinating...

Imagine moving something for 3 metres.

Which is about 1.8*10^35 discrete steps of Plank’s length.

Now, this means that if we would look for just 1 second at every step of that motion it would take us about as much time as the age of Universe multiplied by itself!

(Current best estimate for age of Universe is 13.7 billion years, or 4.3*10^17 seconds).

Does this look amazing just to me?

 

[Chalnoth]

Well, you can't actually do that, though, because the particles that make up the atoms in your body have wavelengths much larger than the Planck length.

 

[Boy@n]

Well, you can't actually do that, though, because the particles that make up the atoms in your body have wavelengths much larger than the Planck length.

Are you perhaps saying that if space-time (ST) is not continuous that maximal number of discrete steps in a motion is limited to the size of smallest particles of object being moved? Which would account to how many discrete steps then? Of order around 10^-15 (which is electron radius in meters). And what if ST is indeed continuous, same thing or?

Strange anyway, since I don't see how size of particles would change that... If something is moved from point A to B so that it makes exactly 1m, then surely it doesn't matter what's the size of object you moved, either it is an electron, a proton or a tennis ball... If the distance traveled is 1m then it means that motion consists of at least number of steps of 1m / Plank's length, considering ST is discrete and more if continuous, right?

 

[Chalnoth]

Are you perhaps saying that if space-time (ST) is not continuous that maximal number of discrete steps in a motion is limited to the size of smallest particles of object being moved?

No, it's not that simple. if space-time is discretized, then it's too small to make a difference. In fact, as I stated earlier, you can't actually have a regular discretized space-time. Instead the points are distributed randomly.

One way of perhaps thinking of it is this. Imagine a single particle. This particle exists as a "wave packet" that is distributed over space. Since we're considering a discretized space-time, this wave packet can only take "location" values at specific points. That is, instead of being a smooth wave, it is made up of a series of more or less randomly-distributed points. As we move forward in time, the wave packet covers a different random distribution of points.

But to make it all a bit more complicated, the discretization is not just in space, but also in time, so that you can't even sensibly talk about what it's doing at one particular instant, but have to take a chunk of time and count up all of the points that randomly fit within that chunk. So we might imagine our "chunk" of time as being one Planck time in length, and call that "now". We can then slowly move our "chunk" of time forward, and one by one, space-time points will fall behind into the past, while new space-time points will become part of the present.

Thus one can't even talk about the particle itself making steps of a Planck length or Planck time, because it is distributed over many space-time points, and stepping a tiny fraction of a Planck length, or moving forward a tiny fraction of a Planck time, can lead to the particle covering many new points in space-time.

This means that as long as the particle has a wavelength much longer than the Planck length, this discretization really doesn't make any difference. It doesn't even make "steps" of a Planck length in size, but much much smaller steps (and the bigger the particle's wavelength, the smaller those steps).