Do we have time because we are moving?

[Taragond]

I searched for an answer already but I didn't find a satisfying answer or even exactly the same question (i believe...if I just didn't get it, please let me know)

OK, now to my question:

As it happens, time moves slower with higher speed and/or higher gravity.
I propose to think of two reference-frames.

1. on earth, moving with it around the sun and with it around the center of our Galaxy which is moving away from the point of big bang...
a) Earth around sun: approximately 100000 kph
b) sun around galaxy: approximately 828000 kph
c) milky way through space: approximately 590 kps

2. as the second reference frame I chose the center of the kosmos and assume, there won't be any gravitation left because it all flew out into space (which is still accellerating it's expansion afaik)

If we would take two perfectly synchronised clocks measuring time from 0 to infinity and put one on earch and one at the center of our universe assuming there it has the absolute speed and gravitational pull of zero each. How much would the measured time differ between these within an hour/day/week/month/year/ (earth time)...

PS: I searched for those numbers, please feel free to replace them with more likely values if I didn't chose well. personally i guess we can't really say how fast our galaxy is moving because we probably can't even see any fixed point in space...But the proposition of space-time really affecting different reference frames to measure the same amount of time differently got me thinking about what might be a "universal standard time".
Also as some say time only exists because of gravity and in conjunction with space (if i remember correctly). Wouldn't that mean that at my proposed center of the galaxy without any gravity or speed, there wouldn't be any time at all?
But how does that work?
If mass and speed slow it down, there should be a maximum "speed of time" unless there is negative mass and speed.

I hope at least I made some sense here...
As much as I love thinking about it, I'm really not much of a physicist :( and have too little time to go into detailed studies regarding physics.

PPS: as english isn't my first language please be patient with me if i made mistakes ;)

 

[phinds]

Your premises are so flawed that the rest of your post is moot.

(1) All motion is relative, not absolute as you seem to think it is.
(2) There is no "center of the kosmos/universe" as you seem to think there is
(3) Time does NOT slow down as you travel faster, it just looks that way to someone in a different inertial frame of reference. You, right this minute, are traveling at .999999c from some frame of reference. From that frame of reference, your time is severely slowed down. From some other frame of reference you are traveling at .9c and your time is only mildly slowed down. From YOUR frame of reference, you time is not slowed down at all. Are any of those three frames of reference more correct than the others? No.

 

[PeterDonis]

Taragond, welcome to PF!

time moves slower with higher speed and/or higher gravity.

This is true only in a relative sense, and it works differently in the two cases you refer to. In other words:

* If you are moving relative to me, then your clocks will seem to me to be running slow, and my clocks will seem to you to be running slow. But your clocks will seem to you to be running normally, and my clocks will seem to me to be running normally.

* If you are closer to a large gravitating mass than I am, and we are not moving relative to each other, then your clocks will seem to me to be running slow, and my clocks will seem to you to be running fast. But your clocks will seem to you to be running normally, and my clocks will seem to me to be running normally.

I propose to think of two reference-frames.

1. on earth, moving with it around the sun and with it around the center of our Galaxy which is moving away from the point of big bang...
a) Earth around sun: approximately 100000 kph
b) sun around galaxy: approximately 828000 kph
c) milky way through space: approximately 590 kps

All of these speeds are relative; there is no such thing as absolute speed. The speed in a) is the Earth's speed relative to the Sun; the speed in b) is the Sun's speed relative to the center of the galaxy; the speed in c) is the galaxy's speed relative to the cluster of galaxies that it is moving towards (I'm not sure which galaxies exactly, I would have to look it up--I also haven't checked your numbers, but the exact numbers don't really matter for this discussion).

2. as the second reference frame I chose the center of the kosmos

There is no such thing; the universe (which is what I think you mean by "kosmos") doesn't have a center.

and assume, there won't be any gravitation left because it all flew out into space (which is still accellerating it's expansion afaik)

The fact that the universe's expansion is accelerating does not mean there is no gravitation left. In fact, the acceleration of the universe's expansion is a form of gravitation (though it's a form that doesn't work the same as the ordinary form of gravitation that we are used to).

If we would take two perfectly synchronised clocks measuring time from 0 to infinity and put one on earch and one at the center of our universe assuming there it has the absolute speed and gravitational pull of zero each. How much would the measured time differ between these within an hour/day/week/month/year/ (earth time)...

It's impossible to answer this question because, as I said above, there is no center of the universe. That means there is also no such thing as absolute time; there is no "true" time that all other times can be measured relative to.

Also as some say time only exists because of gravity and in conjunction with space (if i remember correctly).

Can you give a specific reference for this? "As some say" doesn't help very much, since the statement as you give it is vague and could mean a number of different things.

If mass and speed slow it down, there should be a maximum "speed of time" unless there is negative mass and speed.

Speed is relative, as I said above. Mass is not; if there were only a single isolated mass in the entire universe, there would indeed be a "maximum speed of time", which would be approached as a limit as you got farther and farther away from the mass. However, our universe does not have a single isolated mass; on average, over large distances, it has a relatively constant density of matter everywhere. In such a universe there is no "maximum speed of time"; it's all relative.

As much as I love thinking about it, I'm really not much of a physicist :( and have too little time to go into detailed studies regarding physics.

It's fine to ask questions about things, but you should realize that the concepts you are asking questions about are hard to understand without at least some detailed study. So you may find that you can't really get a satisfying answer to some of your questions without spending a fair bit of time.

 

[ghwellsjr]

Do we have time because we are moving?

Is this another one of those questions inspired by Brian Greene?

 

[Taragond]

Hi, thanks for your fast reply but i hoped for a few more details on how my thinking is wrong (anf of course WHY)

(1) That sounds as if we can be absolutely sure about that. Of course I know all motion is relative to another. But can we be sure there is not even a theoretical standing still in our universe at all?

(2) Isn't there or are we simply not able to detect one? By which theory do you conclude there isn't any center? If there was a big bang, wouldn't the center of that "explosion" also be a kind of center of the universe? Am I still hanging on an old flawed theory or did I misunderstand it?

(3) Isn't it true, that if you put perfectly synchronised watches one on Earth and one on a satellite and bring them back together later, they aren't in sync any more?
Aren't the clocks of our gps-satellites going faster to compensate for the speed they have orbiting us?
Also I didn't ask for "the correct" time but for the difference between them. And that's why i specified frames of reference.
If that's correct so far, am I thinking so flawed that it's not possible to deduct a difference between two hypothetical reference-frames?

And isn't it possible to calculate how different those clocks would be?

Ay, have to read some posts to get the hang of it ;)

 

[Taragond]

Thank you PeterDonis,
that's what I hoped for.

* If you are moving relative to me, then your clocks will seem to me to be running slow, and my clocks will seem to you to be running slow. But your clocks will seem to you to be running normally, and my clocks will seem to me to be running normally.

* If you are closer to a large gravitating mass than I am, and we are not moving relative to each other, then your clocks will seem to me to be running slow, and my clocks will seem to you to be running fast. But your clocks will seem to you to be running normally, and my clocks will seem to me to be running normally.

That's actually pretty much the way I understood it, with the distinction of the actual difference in measured time if you bring the clocks from different reference frames together afterwards...see my last post about gps and co.

All of these speeds are relative; there is no such thing as absolute speed. The speed in a) is the Earth's speed relative to the Sun; the speed in b) is the Sun's speed relative to the center of the galaxy; the speed in c) is the galaxy's speed relative to the cluster of galaxies that it is moving towards (I'm not sure which galaxies exactly, I would have to look it up--I also haven't checked your numbers, but the exact numbers don't really matter for this discussion).

ok, just wanted to give numbers as a basis for calculations if possible but you are right, for the discussen itself they don't matter at all

There is no such thing; the universe (which is what I think you mean by "kosmos") doesn't have a center.

Also ok by me, should have called it a hypothetical center but if that's not possible either, I'm ok with that as well...
Regarding this maybe I should ask if "we" are still considering a big bang or if we moved past that already...

The fact that the universe's expansion is accelerating does not mean there is no gravitation left. In fact, the acceleration of the universe's expansion is a form of gravitation (though it's a form that doesn't work the same as the ordinary form of gravitation that we are used to).

uh, i should have recognised that by myself...accelleration means working forces...of course (facepalm)

Can you give a specific reference for this? "As some say" doesn't help very much, since the statement as you give it is vague and could mean a number of different things.

sorry about that. I saw a few dokumentations recently and one said that time probably began it's own existence with the beginning of the universe, didn't exist before and therefore...there is no "before" the big bang...

It's fine to ask questions about things, but you should realize that the concepts you are asking questions about are hard to understand without at least some detailed study. So you may find that you can't really get a satisfying answer to some of your questions without spending a fair bit of time.

I was aware of that, but from my point of view it's really hard to find the right point to start. As my time is limited I just can't afford to try to learn everything from scratch as much as i want to... :(

 

[MathJakob]

By which theory do you conclude there isn't any center? If there was a big bang, wouldn't the center of that "explosion" also be a kind of center of the universe?

Hubble proved that either the universe doesn't have a centre, or that everywhere is the centre. I too used to think the big bang was an explosion such that space and time would be projected in the shape of a sphere, thus producing a single initial point of creation, when observed, would be the centre of the universe.

This simply isn't the case, as far as we can tell the observable universe is flat...

 

[bapowell]

This simply isn't the case, as far as we can tell the observable universe is flat...

The universe having no center has nothing to do with the universe being flat. The balloon analogy, which imperfectly but sufficiently models an expanding spherical universe, illustrates this point.

Taragond: The big bang did not occur at a single point in a pre-existing space -- it occurred everywhere -- including where you happen to be right now! The observable universe is a uniformly expanding, homogeneous space. The big bang is just the name cosmologists assign to this model of a universe, once hot and dense, that has been expanding and cooling throughout its history.

 

[PeterDonis]

Regarding this maybe I should ask if "we" are still considering a big bang or if we moved past that already...

The Big Bang model is still the accepted model of how the universe began. There are various details still being worked out, but none of them change the overall conclusion that the Big Bang is how the universe began (though some of them redefine exactly what our "universe" that began with the Big Bang is within a larger scheme--see below).

I saw a few dokumentations recently and one said that time probably began it's own existence with the beginning of the universe, didn't exist before and therefore...there is no "before" the big bang...

This is true of what might be called the "standard" model of the Big Bang, but there are other models in which it is not true, such as the "eternal inflation" model in which what we call the "universe" is just one "bubble" within a larger universe in which these inflating bubbles are constantly forming. (String theory's idea of the "landscape" of all possible universes consistent with string theory is also somewhat similar to this.) These are among those details that I referred to above, that are still being worked out.

 

[MathJakob]

The universe having no center has nothing to do with the universe being flat.

I never said it did, I was explaining to the OP how it didn't explode in a spherical shape like he thought.

 

[Maxila]

Hi, thanks for your fast reply but i hoped for a few more details on how my thinking is wrong (anf of course WHY)

(1) That sounds as if we can be absolutely sure about that. Of course I know all motion is relative to another. But can we be sure there is not even a theoretical standing still in our universe at all?

No, because the experimentally verified, theory of relativity tells us that all motion is relative to something.

(2) Isn't there or are we simply not able to detect one? By which theory do you conclude there isn't any center? If there was a big bang, wouldn't the center of that "explosion" also be a kind of center of the universe? Am I still hanging on an old flawed theory or did I misunderstand it?

Observations show that all galaxies (and galaxy clusters) are moving away from each other at the same rate relative to their distance apart. There is no observable central point from which you can look out to see more distance galaxies moving away at a different rate. In other words since that observation will be the same from any point in the Universe, how do you determine and define a center.

Another issue is if the Universe is finite or infinite in size, there is some disagreement; however NASA WMAP data indicates the geometry of the universe is flat and the models that most support that geometry would indicate the Universe is infinite in size. How do you define a center in something infinite in size?

(3) Isn't it true, that if you put perfectly synchronized watches one on Earth and one on a satellite and bring them back together later, they aren't in sync any more?

Aren't the clocks of our gps-satellites going faster to compensate for the speed they have orbiting us?

And isn't it possible to calculate how different those clocks would be?

Yes, yes, and yes as long as you remember it is a matter of perspective. Keep in mind the realtive aspect of time and motion, from the GPS satellite perspective their clock is not fast the Earth clocks are slow. I think the poster was just trying to remind you time only functions at different rate outside your frame of reference and it never change's in it.

 

[bapowell]

Another issue is if the Universe is finite or infinite in size, there is some disagreement; however NASA WMAP data indicates the geometry of the universe is flat and the models that most support that geometry would indicate the Universe is infinite in size. How do you define a center in something infinite in size?

The surface of a sphere is finite, and yet lacks a center. Also, there are flat universes which are compact, like a torus. So the question of whether the universe is infinite or finite doesn't really help here.

 

[Taragond]

Well ok. As we have multiple not yet proven models, I'm not entirely sure what prove there is for simply stating there is no center. But as we surely can't find one I will gladly forget about it.

Am I correct assuming that if we were to reach lightspeed (yep, I know, infinite mass...) time would be standing still if observed from our perspective?

Also what I just don't get into my head, If I were traveling at .5c (for the sake of it not being possible to travel at full light speed). And would turn on head-lights the resulting light would travel away from me with perceived c but also an outside observer standing still would see the same light moving with lightspeed as well an not at 1.5*c? (the last part doesn't need further explaining, what baffles me is why it wouldn't seem to me that it travels at .5c?)

Now to my other issue with the universe...just got it thanks to you guys ;)
What now? We know how that it didn't expand spherical?
And how did it happen everywhere? I understood that once it was compressed in a massive singularity.
Am I seeing space wrong? I assumed, space is just there...no matter no energy, just space. where we are matter and energy fill space...while before the big bang there would be space without anything else in it.
So with your balloon analogy. The balloon would represent the universe. And when it is expanding, it is expanding where? Outside of that balloon would still be space, just with nothing at all in it, or not?

To get somewhat back to my opening premises and maybe better understand time:
a) traveling with .5c
b) traveling with .5c in the opposite direction
c) standing still
Questions:
1. would a) and b) see each other as traveling with c?
2. how would the clocks of a) and b) desynchronize from c) if brought together into the same reference frame after say a hundred years from c) point of view?
3. If it's all relative to the point of view, wouldn't that result in a time difference between a) and b) as well? even a higher one compared to the differences between a):c) and b):c) which should be the same?

PS: I needed some time to formulate this, partly because i was in a late conversation about a software-project for two hours, so between starting and finishing it there were more posts.
Therefore, thank you very much Maxila for answering question 3 of post 5, I already assumed it before my new premises but now i could just start without it :)

In addition I would like to ask about how we can be sure theory of relativity is the end of it? If we were looking from outside the universe (assuming there is an outside ) we could probably see a center which from the inside isn't possible to determine. and If we saw that center from the inside it would of course move in relation to us and we wouldn't know that it's standing still (if of course it can be said that the universe itself isn't moving, but that's much further than i wanted to go in the first place where I just tried to understand time and what effects it how)

 

[bapowell]

Well ok. As we have multiple not yet proven models, I'm not entirely sure what prove there is for simply stating there is no center. But as we surely can't find one I will gladly forget about it.

OK, but it really isn't just an assumption. Sure, there are models that are non-isotropic, but they fail to match observations. We conclude that there is no center because as far back as we can see -- even out to the CMB itself -- the universe appears homogeneous.

Am I correct assuming that if we were to reach lightspeed (yep, I know, infinite mass...) time would be standing still if observed from our perspective?

No, since the equations of special relativity break down at v=c. They simply don't work anymore.

Also what I just don't get into my head, If I were traveling at .5c (for the sake of it not being possible to travel at full light speed). And would turn on head-lights the resulting light would travel away from me with perceived c but also an outside observer standing still would see the same light moving with lightspeed as well an not at 1.5*c? (the last part doesn't need further explaining, what baffles me is why it wouldn't seem to me that it travels at .5c?)

NO! This is the main result of special relativity -- the speed of light in vacuum is equal to c for *all* inertial observers!

And how did it happen everywhere? I understood that once it was compressed in a massive singularity.

There was no singularity. The singularity that everyone associates with the big bang does not refer to a physical reality since it's impossible. Instead, the big bang singularity in cosmology (like the black hole singularity) is signalling that the theory is breaking down at these points. The theory is not applicable, and the physics it predicts is wrong. We simply don't know what happened at t=0.

while before the big bang there would be space without anything else in it.

No, this is the wrong picture. The big bang was not an explosion occurring in a pre-existing space. The big bang is the initial expansion of the space itself.

So with your balloon analogy. The balloon would represent the universe. And when it is expanding, it is expanding where? Outside of that balloon would still be space, just with nothing at all in it, or not?

The universe is the surface of the balloon, so it's necessarily a lower-dimensional analogy. Replace the 2-D surface of the balloon with a 3-sphere and you'll get the model appropriate to our universe. The downside to the balloon analogy is that it implies -- wrongly -- that there is a space inside and outside the balloon. Interestingly, this is not necessary for the universe (for the balloon either, mathematically). It is possible to describe the expanding surface of an n-sphere in n-dimensional space -- no higher dimensional ambient space required!

1. would a) and b) see each other as traveling with c?

No. Look up the relativistic addition of velocities.

2. how would the clocks of a) and b) desynchronize from c) if brought together into the same reference frame after say a hundred years from c) point of view?

How were they all originally synchronized? Bringing them all together into the same reference frame likely requires someone to change direction, which requires acceleration. This complicates the problem somewhat. See the Twin Paradox.

In addition I would like to ask about how we can be sure theory of relativity is the end of it? If we were looking from outside the universe (assuming there is an outside ) we could probably see a center which from the inside isn't possible to determine. and If we saw that center from the inside it would of course move in relation to us and we wouldn't know that it's standing still (if of course it can be said that the universe itself isn't moving, but that's much further than i wanted to go in the first place where I just tried to understand time and what effects it how)

I don't know why you think one would see a center. Why do you suppose this is somehow more natural than a manifold without a center? Where's the center of the surface of the Earth?

 

[Taragond]

No, this is the wrong picture. The big bang was not an explosion occurring in a pre-existing space. The big bang is the initial expansion of the space itself.

so...do most assume there is no "outside"?

The universe is the surface of the balloon, so it's necessarily a lower-dimensional analogy. Replace the 2-D surface of the balloon with a 3-sphere and you'll get the model appropriate to our universe. The downside to the balloon analogy is that it implies -- wrongly -- that there is a space inside and outside the balloon. Interestingly, this is not necessary for the universe (for the balloon either, mathematically). It is possible to describe the expanding surface of an n-sphere in n-dimensional space -- no higher dimensional ambient space required!

oops, ok that is something i will have to wrap my head around before i can assume anything else about it...it just feels easier to imagine an infinite universe with no ends than one where you can walk around in an endless "straight circle"...

NO! This is the main result of special relativity -- the speed of light in vacuum is equal to c for *all* inertial observers!

No. Look up the relativistic addition of velocities.

After reading on wikipedia (i hope http://en.wikipedia.org/wiki/Velocity-addition_formula is what you meant) my thinking would go as follows:
the light leaving observer a's reference frame becomes its own reference frame?
and because of the time dilution every reference frame would measuere the speed of said light at the same velocity?
also, even looking it up i sadly can't make anything of the formulas at what speed would i measure someone coming straight at me with .5c while I'm heading straight towards him at .5c?

How were they all originally synchronized? Bringing them all together into the same reference frame likely requires someone to change direction, which requires acceleration. This complicates the problem somewhat. See the Twin Paradox.

ok, they were synchronized at oberserver c) then a) and b) accelerate to .5c in opposite direction where each of them stop when about a lightyear away. then they turn and accelerate the same way to get back to c) where they compare their clocks ( I would just say they accelerate instantly just to simplify the calculation if that is mathematically possible, i know it isn't physically)

I don't know why you think one would see a center. Why do you suppose this is somehow more natural than a manifold without a center? Where's the center of the surface of the Earth?

well, probably because it's more natural to me, but you are right of course, i don't have any knowledge about how the universe looks like as a whole...if it's infinite it wouldn't even have a shape at all but would you deem it more likely it is just infinite in any direction or do you suppose if you would fly in one direction you eventually would get back at where you started?

 

[PeterDonis]

Am I correct assuming that if we were to reach lightspeed (yep, I know, infinite mass...) time would be standing still if observed from our perspective?

No, because "time" from the perspective of an object moving at lightspeed is a meaningless concept. For example, there is no such thing as "time from a photon's perspective".

What this really means is that objects that move at lightspeed are fundamentally different, physically, from objects that move slower than light. "Time", or more precisely "proper time", which is the technical term for "time from the object's perspective", is a concept that only applies to the latter kind of object.

 

[Nugatory]

also, even looking it up i sadly can't make anything of the formulas at what speed would i measure someone coming straight at me with .5c while I'm heading straight towards him at .5c?

His speed is .5c relative to what? And your speed is .5c relative to what? Any time you're thinking about speeds without paying attention to what they're relative to, you'll find yourself in trouble with relativity.

So let's try phrasing your question more precisely: there is an observer, who is (of course) at rest relative to himself. You are approaching this observer from his left at .5c relative to him. Someone else is approaching him from his right at .5c relative to him. What do you see?

Well, you are rest relative to you. You see the observer rushing towards you at .5c relative to you. And beyond the observer you see the other guy, moving even faster relative to you. How fast? That's what the velocity addition formula is for:
<br /> \frac{u+v}{1+\frac{uv}{c^2}} \Rightarrow \frac{.5c+.5c}{1+\frac{(.5c)(.5c)}{c^2}} = .8c<br />

 

[ghwellsjr]

Also what I just don't get into my head, If I were traveling at .5c (for the sake of it not being possible to travel at full light speed). And would turn on head-lights the resulting light would travel away from me with perceived c but also an outside observer standing still would see the same light moving with lightspeed as well an not at 1.5*c? (the last part doesn't need further explaining, what baffles me is why it wouldn't seem to me that it travels at .5c?)

I think it might help you to understand with the aid of a series of spacetime diagrams.

First, I'll draw one that describes your scenario. There is an outside observer standing still at the coordinate position of zero depicted in blue. The dots along his worldline indicate one-nanosecond increments of time. You are depicted in red and your dots are Time Dilated to 15% longer distances due to your speed of 0.5c. (The calculation is for the Lorentz factor, in case you're interested.) At the origin of the diagram (when all the coordinates and clocks equal zero and where the observer is), you turn on your head-lights we'll say for a brief moment just to make an identifiable burst or flash of light which is shown as the thin red line extending up and to the right along a 45-degree diagonal. Light travels at one foot per nanosecond. Here's the first spacetime diagram:

Have you ever considered what it takes to "perceive" or "see" (your words) a flash of light? As a matter of fact, once it leaves you, there is no way for you to watch it as it travels away from you, is there? Instead, what you can do is place an object along the light's path and then you will be able to see the reflected flash when it finally gets back to you. Then, you can measure how far away the object was from you with your ruler or yardstick and you can measure how long the total round trip time was for the flash to leave your vicinity, travel to the object and reflect off of it and travel back to you. If you make the assumption (Einstein's convention) that the light took the same amount of time to travel away from you as it did to travel back to you, then you can easily determine the speed of light from your measurements.

Let's see how this works for the outside observer as he measures the flash from one of your head-lights. Let's assume that he has placed a reflector one yard (three feet) away from himself. Then the light will reflect back to him as shown in this diagram (we'll assume the flash from the other head-light continues on):

The green worldline is his reflector. Notice it is also stationary in his rest frame and it remains 3 feet away from him. The light takes 6 nsecs to make the round trip from the origin to the green reflector and back to him. He assumes that the light spent half its time getting to the reflector and half it time getting back and concludes that the light traveled 3ft/3nsec for a speed of 1 foot per nanosecond, the correct answer.

Now let's see how you would make a similar measurement. We'll start over again and focus on just what you would do. First off, we need to transform the scenario to your rest frame using the Lorentz Transformation process (which is just a set of equations that we apply to all the events (dots) in the diagram. Notice how your time is no longer dilated but lines up with the Coordinate time while the observer's time is dilated. You will have stuck a reflector (shown in black) on a structure that extends out one yard in front of your car and you exactly perform the same measurements that the original observer did and arrive at the same conclusion that light travels at one foot per nanosecond. Does this make sense to you?

Now we go back to the original rest frame to see what your measurement looks like in the starting frame:

You can see that in this frame, your reflector has moved up and to the right but closer to you, allowing light to travel at "c" and still arrive at the same 6-nsec final time.

Now for some real fun. I'm going to show the frame of the first diagram with all the obects, observers, and light paths and show how in this one frame, both the observer and you determine the speed of light to be c:

You should be able to identify all the details of the two sets of measurements by the observer and you and the calculations leading to the speed of light. If so, you are ready to see the last diagram, that of your rest frame with both sets of measurement going on at the same time and both leading to the same conclusion for the speed of light, c:

Does this help clear up your confusion?

 

[Taragond]

His speed is .5c relative to what? And your speed is .5c relative to what?

Both speeds are relative to c) which i assumed to be standing still

Well, you are rest relative to you. You see the observer rushing towards you at .5c relative to you. And beyond the observer you see the other guy, moving even faster relative to you. How fast? That's what the velocity addition formula is for:
<br /> \frac{u+v}{1+\frac{uv}{c^2}} \Rightarrow \frac{.5c+.5c}{1+\frac{(.5c)(.5c)}{c^2}} = .8c<br />

wow, that adds up to .8c?
What if:

a) and b) are both half a lightyear away from c) while a whole lightyear away from each other.
Then both are instantly accelerated to .5c towards c)
Both should arrive at c) one year later?

So if c) wasn't there, they would arrive at each other exactly one year later? If they were able to measure their exact distance before accelerating they would conclude that they approached each other with c, wouldn't they?

@ghwellsjr: wow, that was really helpful... while I was aware of the difficulty to "see" light in a vacuum I didn't think it would matter for theorization.

But it raised one question.
I assumed before that the light would seem to be moving away from me with .5c
They way some of those diagrams look could suggest (as I suspected before) that the light travels a longer way to the mirror I have on my "car" as it travels back to my sensor (but only to the observer outside because in this construct, my mirror doesn't measure the time when it reflects the light)
Is it just very probable or can we be absolutely sure that if:
I were to travel at .5c with my long straight train.
Two extremely prezise synchronized clocks, both with a flashlight and a sensor are placed a fair distance away on that train so there can't be any difference between the way towards a mirror and back to a sensor, that they would measure the same amount of time for the light of each others flashlight reaching the other sensor?

PS: Sorry if I'm annoying ;)

 

[Nugatory]

wow, that adds up to .8c?

Sure does... But don't take my word for it, try it yourself.

Also, it's interesting to see what happens if either of the speeds are $c$; that covers the situation in which both you and an observer moving relative to you get the same speed $c$ for a light signal.

 

[ghwellsjr]

@ghwellsjr: wow, that was really helpful... while I was aware of the difficulty to "see" light in a vacuum I didn't think it would matter for theorization.

It's not just difficult, it's impossible, not only to see the propagation of light but also to know where it is at any given time unless we do as Einstein said to do, we define the time that light arrives at a distant locatoin.

But it raised one question.
I assumed before that the light would seem to be moving away from me with .5c

You can make that assumption, but if you do, you will be lead to the conclusion that it travels instantly on its way back to you, based on your measurement of the roundtrip time, correct? For example, if you measured 6 nsecs for it to make the roundtrip between your car and your mirror three feet away, and you assume that it traveled at 0.5c away from you, then you are saying that it took 6 nsec to get there but since you see it get back to you in 6 nsec, the trip back has to be instantaneous.

They way some of those diagrams look could suggest (as I suspected before) that the light travels a longer way to the mirror I have on my "car" as it travels back to my sensor (but only to the observer outside because in this construct, my mirror doesn't measure the time when it reflects the light)

That is correct, your mirror doesn't measure the time when the light is reflected. And remember, the outside observer has the same problem you have, he can't see the propagation of light either and he has to make an assumption just like you do.

Is it just very probable or can we be absolutely sure that if:
I were to travel at .5c with my long straight train.
Two extremely prezise synchronized clocks, both with a flashlight and a sensor are placed a fair distance away on that train so there can't be any difference between the way towards a mirror and back to a sensor, that they would measure the same amount of time for the light of each others flashlight reaching the other sensor?

As I said before, "there is no way for you to watch it as it travels away from you" and that includes there is no way for you to know how light moves away from you.

You suggest two extremely precise synchronized clocks a fair distance away from each other but you haven't described how you can get them to be synchronized so that you can make the measurement and that is the issue. Einstein's solution is for you to make the measurement and if it doesn't come out so that the times are equal, you adjust one of the clocks so that it does come out equal the next time you make the measurement. In other words, making the measurement repeatedly is how you get the clocks to be synchronized. Does that make sense to you?

PS: Sorry if I'm annoying ;)

As long as you're learning, you're not annoying.

 

[ghwellsjr]

To get somewhat back to my opening premises and maybe better understand time:
a) traveling with .5c
b) traveling with .5c in the opposite direction
c) standing still
Questions:
1. would a) and b) see each other as traveling with c?

In my previous post, I made some diagrams to show how you and the outside observer both determine the speed of light by making measurements, making an assumption and doing a calculation.

It's different when observers are trying to determine the speeds of other observers. They can't just make observations, they have to actively generate some signals that we call radar signals and measure the timings of the reflections and then make some more assumptions about the radar signals and do some calculations. This is known as the radar method and I used it to answer the same question as yours that someone else asked a while back. I also made several spacetime diagrams which I hope made it all clear. Have a look at this thread:

Frames of reference for speed?

Let me know if this answers your question.

2. how would the clocks of a) and b) desynchronize from c) if brought together into the same reference frame after say a hundred years from c) point of view?
3. If it's all relative to the point of view, wouldn't that result in a time difference between a) and b) as well? even a higher one compared to the differences between a):c) and b):c) which should be the same?

I also answered similar questions to yours in this thread:

Triplet Paradox

That thread has a lot of side issues so I would suggest that you just zip past them and get to where I show my diagrams on page 6 and 8. (That thread was what motivated me to write my software to do these diagrams and you can see how my diagrams have evolved.)

Let me know if you have any more questions.

 

[xcourrier]

What if:

a) and b) are both half a lightyear away from c) while a whole lightyear away from each other.
Then both are instantly accelerated to .5c towards c)
Both should arrive at c) one year later?

So if c) wasn't there, they would arrive at each other exactly one year later? If they were able to measure their exact distance before accelerating they would conclude that they approached each other with c, wouldn't they?

If c) was there, its perfectly alright that he measure both a) and b) as moving at .5c. It is also true that if a) and b) were "still," (meaning sharing c)'s reference frame) they could measure the distance between them as 1LY. However once moving, from the perspective of a) and b), the original distance between them would no longer have been 1LY, and they would not be traveling at 1c towards each other, as they changed their frame of reference (even though that is exactly what c) measures)

 

[Nugso]

Taragond, welcome to PF!



This is true only in a relative sense, and it works differently in the two cases you refer to. In other words:

* If you are moving relative to me, then your clocks will seem to me to be running slow, and my clocks will seem to you to be running slow. But your clocks will seem to you to be running normally, and my clocks will seem to me to be running normally.

* If you are closer to a large gravitating mass than I am, and we are not moving relative to each other, then your clocks will seem to me to be running slow, and my clocks will seem to you to be running fast. But your clocks will seem to you to be running normally, and my clocks will seem to me to be running normally.

Hello. I have a question I'd like to ask if I may, so basically if you and I have watches and you were to move relative to me with a velocity of 0.9c, I'd see your watch run slower than it would run when you don't move relative to me, and you'd still see your own watch run normal? Did I get it right? If yes, how would I see it run slow? Doesn't something like a battery of the watch have to be low so that I can see your watch run slower?

 

[ghwellsjr]

What if:

a) and b) are both half a lightyear away from c) while a whole lightyear away from each other.
Then both are instantly accelerated to .5c towards c)
Both should arrive at c) one year later?

Yes, according to the frame in which all three were originally at rest and according to c)'s clock (since he remained at rest), but not according to the clocks that a) and b) carry with them. According to their clocks, they arrive in 10.4 months. This can be determined by dividing 12 months by the Lorentz Factor at 0.5c (12/1.15471=10.4).

So if c) wasn't there, they would arrive at each other exactly one year later?

Of course if we removed c) and his clock from the scenario, then there won't be any clock that reads one year when a) and b) unite but it's still the case that in the original IRF the time is one year when they arrive together and it's still the case that their own clocks read 10.4 months.

If they were able to measure their exact distance before accelerating they would conclude that they approached each other with c, wouldn't they?

They can measure their exact distance between each other all along the way but they won't measure that they approached at c. In fact, the maximum speed that they each see the other one approaching is 0.8c (the relativistic sum of 0.5c and 0.5c) but they also measure two other speeds. They can also measure their distance to c) and his approach to them (maximum of 0.5c). Here, I'll show you how this works.

First we start with a spacetime diagram depicting your scenario in the original Inertial Reference Frame (IRF). The thick blue line represents a), the thick black line represents c) and the thick green line represents b). The dots show one-month intervals of the passage of time for each observer and his clock. I have also drawn in some radar signals to show how a) measures how far away c) is as a function of his own time:

It's important to realize that a) has been sending and receiving radar signals continually during the entire scenario and he would typically process them all but that would make for a very cluttered diagram so I only show enough to get the relevant point across. Here is a list of the measurements a) makes along with his calculations:

Radar   Radar   Calculated   Calculated   Black's
Sent    Rcvd      Time        Distance     Time
-24     -12       -18            6         -18
-12       0        -6            6          -6
  0       6.9       3.45         3.45        6
 10.4    10.4      10.4          0          12

Just by way of reminder, the Calculated Time is the average of the Radar Sent and Radar Rcvd times and the Calculated Distance is the difference between those two times divided by two. Black's Time is simply what a) observes at the Radar Rcvd time.

Now all the time that a) is making the radar measurements to c), he is doing the same thing with b). Here's a diagram showing these measurements:

And here is his list of measurements and calculations:

Radar   Radar   Calculated   Calculated   Green's
Sent    Rcvd      Time        Distance     Time
-24      0        -12           12         -12
-12      6.9       -2.55         9.45        0
  0      9.2        4.6          4.6         6.9
 10.4   10.4       10.4          0          10.4

Now before I show you a diagram depicting the results from the two tables, I want to show you another IRF for the final rest frame of a):

Note how all the measurements from the previous IRF continue to be the same in this IRF and particularly note the measurements made by a) while he was at rest at the top end of the diagram.

Now here is the diagram showing what a) determines from his measurements, the assumption that a radar signal always takes the same amount of time to reach its target as it does to return the echo, the observation of the target's clock and the calculations defined as the radar method:

Note how a) is at rest in this non-inertial frame and how c) and b) are moving towards him. Even though this frame is non-inertial, it still adheres to the defined rule that light (and radar signals) always travel at c. However, even though we see the dots indicating deviations from coordinate time, they aren't always dilated, sometimes they are constricted. This is because this frame was not derived from an application of the Lorentz Transformation.

Now I want to show you that the radar signals are depicted faithfully in this non-inertial frame, just like they are in any IRF. Here's the first diagram repeating measurements of c):

And finally a diagram repeating the measurements of b):

In particular, note that the top end of this diagram exactly matches the top end of the third diagram in this post (not the coordinates, just the relative shapes and positions of all the features) and the bottom end of this diagram exactly matches the bottom end of the second diagram.

If you want, you can determine the intermediate speeds of b) and c) as they approach a). And I'm sure you're aware that these diagrams are mirror images of what we would draw for b) measuring the positions and speeds of a) and c).

Any questions?

 

[Taragond]

Hi ghwellsjr,
sorry for my long absence!
I'm really struggling with making the time for this, and having still enough plasticity of mind to at least think I might understand ;)

What I think to have found out...most of my general problems (besides mathematics, obviously) with this seem to have originated in my failure to understand why I would "see" light always as moving with c...
Of course, if I'm moving faster I percieve time as I do when standing still...so anything theoretically moving slower compared to me than to the still observer (from his perspective) would seem faster to me (from my "slowed down" perspective)...don't ask me how I could overlook that, I have NO IDEA :D

Thank you again for your patience :)

PS: I'm sorry I didn't make it back earlier to thank you properly for investing your time :(

 

[Maxila]

What I think to have found out...most of my general problems (besides mathematics, obviously) with this seem to have originated in my failure to understand why I would "see" light always as moving with c...
Of course, if I'm moving faster I percieve time as I do when standing still...so anything theoretically moving slower compared to me than to the still observer (from his perspective) would seem faster to me (from my "slowed down" perspective)...don't ask me how I could overlook that, I have NO IDEA

In case you also weren't aware (I didn't see you mention it) when your time is relativity slower to another observer via being in a stronger gravitational field, or having a higher relative motion there is length contraction which is proportional to your time. In other words if another observer saw your time as t/2 (one half the rate of theirs), both of you would observer the distance between you differently, where they saw the distance between you as x you you'd observer the distance as x/2 (proportional to the time difference between both of you).

That's one dynamic (length contraction) to explain how c remains unchanged for both observers who experience different rates of time, not only do they experience time differently, length is observed differently too, also solidifying the absolute connection between space and time.

 

[PeterDonis]

when your time is relativity slower to another observer via being in a stronger gravitational field, or having a higher relative motion there is length contraction which is proportional to your time

This is not true for a gravitational field. (The way you've stated it is a little garbled even for relative motion.)

 

[Maxila]

This is not true for a gravitational field. (The way you've stated it is a little garbled even for relative motion.)

See: http://www.mth.uct.ac.za/omei/gr/chap8/node8.html and credentials @ http://www.mth.uct.ac.za/~peter/Peter_Dunsby/About_me_1.html

 

[Taragond]

What now? I knew of length contraction but only ever thought about it as observer C would see A and B shorter than they "are".

To clarify that without involving a gravitational field. And I hope it is a reasonable preset...
suppose
observer A rests.
observer B moves circular around A with .4c and .4c radius
observer C moves circular around A with .8c and .8c radius
(A, B and C have aside from that the same properties (when standing still))

A would now see B and C with their respective v and r. while C seems to be shorter than B!?
B would see A longer and C shorter!?
C would see B shorter than A but both longer than himself!?

Now what I didn't even consider before...

A, B and C would each perceive distances between them differently? (I can imagine the problems to even measure that distance if light travels for almost half a year from one to another...especially because it will very probably miss... ;))
on a side note: if all three have clocks on board and transmit a video-signal of that clock... every receiver would literally see the clocks ticking at different speeds? I'm pretty sure, yes, but I'm still in a stadium where I'd like confirmation on every turn :D

 

[PeterDonis]

See: http://www.mth.uct.ac.za/omei/gr/chap8/node8.html

This just shows that calling the effect described "length contraction" is a common misstatement. To see why it's a misstatement, compare the situation in a gravitational field to the situation with relative motion.

(A) Relative motion: you and I are moving past each other at some velocity $v$. Each of us carries a meter stick which, to us, is exactly 1 meter long. As we pass each other, you will measure my meter stick to be shorter than 1 meter, and I will measure your meter stick to be shorter than 1 meter. The key points are (1) we each can make direct measurements, because we are spatially co-located as we pass each other; and (2) the length contraction is symmetric: each of us measures the other's meter stick to be shorter.

(B) Gravitational field: you are out in empty space, far away from all gravitating bodies, and I am down in the gravity well of some large mass. Each of us carries a meter stick which, to us, is exactly 1 meter long.

(1) The first problem is that, unlike in the above scenario, we are not spatially co-located, so there is no direct way for either of us to measure the length of the other's meter stick. The equation on the page you linked to implicitly assumes that there is. But if you try to specify the actual measurement procedure, you will run into difficulties. (A question to consider: in the equation on the page you linked to, which of $ds$, $dr$ represents the length of the meter stick as I measure it? As you measure it?)

For example, suppose you take a second meter stick, and put it alongside your original one, and verify that they are both exactly the same length. Then you lower the second meter stick to me, very slowly and carefully so that its length remains constant. When it reaches me, I put it alongside my meter stick, and guess what? I find that it is exactly the same length as my meter stick.

Now of course you could claim that the second meter stick got "shrunk" as it was lowered into the gravitational field; but this kind of "shrinking", since it affects everything, including any possible measuring instrument, is not directly observable; it's an interpretation that you can put on the equations, but only an interpretation, and not one that's necessary for doing any physics.

(2) The second problem is that, unlike in the scenario with relative motion, the "length contraction" due to the gravitational field is not symmetric. My meter stick "appears" shorter to you, but your meter stick "appears" longer to me. So again, whatever is going on here, it's clearly not the same kind of thing as length contraction due to relative motion, which, as above, is symmetric.

Finally, you might ask: wouldn't the same arguments apply to time dilation in a gravitational field? The answer is no, and it's instructive to consider why. Suppose you and I are situated as above, and we are at rest relative to each other and to the gravitating mass; we can verify this, for example, by exchanging light signals and finding that the round-trip travel time of those signals remains constant. But we will also find that that round-trip travel time is shorter for me than for you: i.e., a given light signal takes longer, by your clock, to make a round trip between us than it takes by my clock. This is a direct measurement that each of us can make, and it gives a direct way of showing how my clock "runs slow" relative to yours. (Once again, this is not symmetric--your clock runs fast relative to mine--so it's not the same kind of thing as time dilation due to relative motion.)

 

[Maxila]

Peter, you’ve made way too much of discussion out of the simple fact I pointed out, it is an axiom of the highest order; as time is variable and relative, length (space) is too, regardless of whether they are changed due to relative motion or gravity, they are both changed in unison and proportionally.

Putting that meter stick aside, for gravitational length contraction one could verify the length difference via the time it would take for a reflected light beam to make the round trip between observer's. The observer in the gravitational field would measure the length between them as being shorter.

 

[phinds]

Hello. I have a question I'd like to ask if I may, so basically if you and I have watches and you were to move relative to me with a velocity of 0.9c, I'd see your watch run slower than it would run when you don't move relative to me, and you'd still see your own watch run normal? Did I get it right?

yes

If yes, how would I see it run slow? Doesn't something like a battery of the watch have to be low so that I can see your watch run slower?

The watch is running at one speed in the frame of reference of the watch and at another speed in another frame of reference. What could a battery have to do with that? You are confusing local observations with remote observations. They don't agree, and that's just a fundamental fall-out of the fact that light moves at the same speed in all frames of reference.

 

[ghwellsjr]

Hi ghwellsjr,
sorry for my long absence!
I'm really struggling with making the time for this, and having still enough plasticity of mind to at least think I might understand ;)

What I think to have found out...most of my general problems (besides mathematics, obviously) with this seem to have originated in my failure to understand why I would "see" light always as moving with c...
Of course, if I'm moving faster I percieve time as I do when standing still...so anything theoretically moving slower compared to me than to the still observer (from his perspective) would seem faster to me (from my "slowed down" perspective)...don't ask me how I could overlook that, I have NO IDEA :D

It's really easy to overlook things that are going on with relativity. The only safe thing to do is precisely specify whatever scenario you are interested in according to an Inertial Reference Frame (IRF) and then use the Lorentz Transformation process to see what it looks like in another IRF. So let's do that with what I think you are describing here although since you weren't very precise, I may not be addressing your issue.

I'm assuming that you have started with the IRF of the "still observer" and you are traveling at some high rate of speed (0.8c) while some other thing is traveling slower than you (0.5c), correct? I'll show the still observer in blue, you are in green and that other thing is in red:

Now you have concluded that since your time is dilated in this frame, you will perceive that the time for that other object will be faster than your time according to your rest frame, correct? Well let's transform to your rest frame and see what happens:

As you can see, the time for that other thing as shown by the spacing of the red dots is dilated even in your rest frame. Does this make sense to you? Or did I misunderstand your scenario?

Thank you again for your patience :)

PS: I'm sorry I didn't make it back earlier to thank you properly for investing your time :(

You're welcome.

 

[ghwellsjr]

(A) Relative motion: you and I are moving past each other at some velocity $v$. Each of us carries a meter stick which, to us, is exactly 1 meter long. As we pass each other, you will measure my meter stick to be shorter than 1 meter, and I will measure your meter stick to be shorter than 1 meter. The key points are (1) we each can make direct measurements, because we are spatially co-located as we pass each other; and (2) the length contraction is symmetric: each of us measures the other's meter stick to be shorter.

Don't you think saying that we can make direct measurements of the length of a moving object can be misleading? No matter how we do it, we have to make some assumption, usually applying Einstein's second postulate (or equivalent), make some measurements and do some calculations to establish length. It's not like we can just lay a meter stick down next to the moving meter stick and directly see that the moving one is shorter like we could if we were measuring the length of a stationary yardstick with our meter stick.

 

[harrylin]

B [..] .. while I was aware of the difficulty to "see" light in a vacuum I didn't think it would matter for theorization. [..]

Actually, in practice you can see light in a near vacuum by means of scattering; cloud chambers are even how particle physics started!
But that's besides the point. What matters is that, while you can trace the sequence of events, you cannot determine the times in an "absolute" way; it all depends on your clock synchronization. In other words, you typically set your clocks in such a way that they agree with the mirror procedure.

 

[Taragond]

As you can see, the time for that other thing as shown by the spacing of the red dots is dilated even in your rest frame. Does this make sense to you? Or did I misunderstand your scenario?

Actually I think it does, although I'm not sure to what scenario you were referring. In your quotation of my previous post I just wanted to say, that while a standing observer would see the light emanating from my headlights being only .5c faster than me (if I'm at .5c) because of my timedilution these .5c would still seem to be c faster than myself. At least that what I think I had understood...

Anyway, your tables made it clear to me, that from the perspective of anyone, without seeing the timeframe of the others and being in empty space without any reference-points than the tree Observers. To both the blue and green Observers it could seem they themselves are standing still while the others are moving? :D only the red one would know that one is slower while the other is faster than himself? (EDIT: I believe I made an error, as the red one could also believe he's standing still while the others are at the same speed moving in different directions, correct?)

Because in my last scenario I deliberately chose to fly in circles around observer A so the distances between them would always be the same. Unfortunately I didn't do the math how fast B and C would have to go to always have a straight line from A to C with B inbetween, so I chose .4 and .8 c respectively, just as an example.

At last, the scenarios measuring a meter-stick got me thinking. What if the meter-stick would instead be a sqare of 1m²? Wouldn't that be a possibility to measure it? Or am I wrong in assuming the reduction in length would only occur parallel to the movement?

Actually, in practice you can see light in a near vacuum by means of scattering; cloud chambers are even how particle physics started!
But that's besides the point. What matters is that, while you can trace the sequence of events, you cannot determine the times in an "absolute" way; it all depends on your clock synchronization. In other words, you typically set your clocks in such a way that they agree with the mirror procedure.

That's what happens in our atmosphere with laserpointers (especially strong with the green ones or ist that only because our eyes are more succeptible to green light?) right?
The time-determination in absolutes wasn't really what I was going at, only compared to each other. Wouldn't it be possible to observe the difference via a video-signal (alright, probably overkill, as it might be easier to just send the timestamp every (own) second.

For the sake of an argument, I will reduce my last scenario and add to it:

Consider only two observers.
A at rest.
B at .9c on a circular orbit around A sending a typical video-signal at 24 fps of his clock (or whatever really)

Would A only receive said signal with less than 24 fps? I guess so...

 

[PeterDonis]

Don't you think saying that we can make direct measurements of the length of a moving object can be misleading?

Not really. True, we can't lay the two meter sticks side by side; but we could, for example, fire a strobe light and take a very quick picture of the moving stick passing by the stationary one, and then compare their lengths in the picture. Or we could have the moving stick trigger two sets of stationary stop clocks as it passed (one set for the front end of the stick, the other for the rear), and then use the stationary meter stick to measure the distance between two stop clocks that show the same time.

One could always say that these measurements are not "direct" because they involve some kind of calculation or assumption; but you could say the same thing about laying the two meter sticks side by side if both were stationary--you have to assume that the light propagating from the sticks to your eyes behaves in a certain way, so that it's giving you accurate information about how the sticks are positioned spatially. In principle, no measurement is ever "direct" in a pure sense; there are always intervening variables and assumptions.

However, if we compare laying two stationary meter sticks side by side to compare their lengths, with comparing the lengths of two stationary meter sticks that are very far apart, so we can't lay them side by side, it seems obvious that the first measurement is "direct" in a way that the second is not. No matter how we do the second measurement, it is going to involve a measurement of one meter stick that has to be done over a large spatial distance. (I'm assuming we aren't "cheating" by, for example, having someone measure the second meter stick's length locally and then transmit the result by radio--the measurement of the second meter stick's length has to be a real remote measurement, for example by measuring the angle it subtends in the visual field of an observer co-located with the first meter stick.) In other words, the second measurement will necessarily involve extra intervening variables and assumptions, compared to the first, and these extra intervening variables and assumptions will involve, not just the meter sticks or the way the measurements are done, but properties of spacetime itself. (For example, if we measure the length of a spatially distant meter stick by measuring the angle it subtends in our visual field, we have to make an assumption about the geometry of spacetime in between, in order to correctly model the relationship between visual angle and length.)

Perhaps the word "direct" isn't the best word to refer to the difference I just described; but that's the difference I was talking about.

 

[ghwellsjr]

Not really.

I don't disagree with what you say (I've learned not to) but I still think what you added can be misleading and I'll explain why.

True, we can't lay the two meter sticks side by side; but we could, for example, fire a strobe light and take a very quick picture of the moving stick passing by the stationary one, and then compare their lengths in the picture.

Yes, it is possible to do this but only if the strobe fires at a very specific time that isn't at all obvious.

Also, you state that the meter sticks are carried by the observers and you imply that they are taking pictures with their cameras with illumination provided only by a strobe light. This, of course, is impossible. The meter sticks must be passing at some distance from the observers (and their cameras) which means that there will be light delay times that must be taken into consideration. I assume that this is what you had in mind. You also didn't state where the strobe light was in relation to the cameras or if there were two separate strobe lights.

But if we focus on just one observer who has a strobe light and camera colocated with him and his meter stick which is held out in front of him some distance away so that the camera can capture an image of both ends of the meter stick within its field of view, plus a little more to capture an image of the moving meter stick if necessary. Of course we assume that both ends of the meter stick are equidistant from the strobe light and camera and that the camera is aimed at the center of the meter stick and that the film in the camera is flat so that if we take a picture of his stationary meter stick the markings on it will be equally spaced. This is in contradiction to the notion that we are measuring the angles at which the light is entering the camera. We also assume that the moving meter stick is essentially lined up with the stationary meter stick and will pass by it either slightly above or below it.

Now we are ready to take a picture. How do we do that? First of all, we open the shutter of the camera and fire the strobe and after sufficient time close the shutter. We assume that no light from the strobe can directly enter the camera and only reflected light does. But we can also be sure that no matter when we fire the strobe, the image of the stationary meter stick will appear the same. We don't have to make any assumptions about the speed of the light or whether it is the same in both directions, agreed? We do have to assume that it goes in a straight line after it gets reflected from a target on its way back to the camera and inside the camera.

But it's a different story for the moving meter stick. In order to get the correct image that shows the Length Contraction of the moving meter stick as measured by the stationary meter stick, we must fire the strobe at just one instant in relation to the moving meter stick such that the images of the ends of the moving meter stick are equidistant from the images of the ends of the stationary meter stick. If the strobe is fired earlier than that, the image of the moving meter stick will be too short and if it is fired later, the image of the moving meter stick will be too long, agreed? That's because when it is approaching, the leading edge of the meter stick will be taken at an earlier time than the trailing edge which will have moved closer to the camera. When receding, the trailing edge will be taken at an earlier time than the leading edge which will have moved farther away from the camera. For the same reason, even for the image that shows the correct overall Length Contraction, the image of the center of the moving meter stick will not coincide with the image of the center of the stationary meter stick. It will appear closer to the trailing edge of the moving meter stick. The markings on the image of the moving meter stick will not be equally spaced as they are on the stationary meter stick. So this image will not correctly show the Length Contraction of all parts of the moving meter stick.

Of course, it is easy to tell if we have taken a correct image but it is not easy to take that correct image. And we can just keep firing the strobe hoping to get a correct image, we have to repeat the experiment over and over again until we get lucky. Or else we have to get smart and wire up a trigger and maybe a delay timer to detect when the meter stick is approaching to fire the strobe at just the right time.

But even after we have done all that and gotten our image that shows the moving meter stick symmetrically centered on the stationary meter stick, we must make it clear that we have assumed that the light takes the same amount of time to travel away from the strobe as it does to get back to the camera. This is the assumption that I said we must make in post #35, that of applying Einstein's second postulate.

Or we could have the moving stick trigger two sets of stationary stop clocks as it passed (one set for the front end of the stick, the other for the rear), and then use the stationary meter stick to measure the distance between two stop clocks that show the same time.

Yes, but let's make it clear that we have also applied Einstein's second postulate to synchronize our stop clocks before hand.

One could always say that these measurements are not "direct" because they involve some kind of calculation or assumption; but you could say the same thing about laying the two meter sticks side by side if both were stationary--you have to assume that the light propagating from the sticks to your eyes behaves in a certain way, so that it's giving you accurate information about how the sticks are positioned spatially. In principle, no measurement is ever "direct" in a pure sense; there are always intervening variables and assumptions.

Yes, but one of those assumptions is not Einstein's second postulate, correct? We do have to assume that the light travels in a straight [line] from the ends of the objects to our eyes but we don't care even if the speed is constant, correct? So there is a fundamental difference between making measurements with objects at rest with the observer and objects in motion, correct?

EDIT: inserted "line" above.

However, if we compare laying two stationary meter sticks side by side to compare their lengths, with comparing the lengths of two stationary meter sticks that are very far apart, so we can't lay them side by side, it seems obvious that the first measurement is "direct" in a way that the second is not. No matter how we do the second measurement, it is going to involve a measurement of one meter stick that has to be done over a large spatial distance. (I'm assuming we aren't "cheating" by, for example, having someone measure the second meter stick's length locally and then transmit the result by radio--the measurement of the second meter stick's length has to be a real remote measurement, for example by measuring the angle it subtends in the visual field of an observer co-located with the first meter stick.) In other words, the second measurement will necessarily involve extra intervening variables and assumptions, compared to the first, and these extra intervening variables and assumptions will involve, not just the meter sticks or the way the measurements are done, but properties of spacetime itself. (For example, if we measure the length of a spatially distant meter stick by measuring the angle it subtends in our visual field, we have to make an assumption about the geometry of spacetime in between, in order to correctly model the relationship between visual angle and length.)

Would you consider it cheating if we applied the standard of the length of a meter using a cesium clock to count out a specific number of cycles to time how long it takes for light to travel one meter? If not, how do propose to calibrate these two meter sticks that are so far apart that we can't compare them by transporting a standard meter stick between them (or something equivalent)?

Perhaps the word "direct" isn't the best word to refer to the difference I just described; but that's the difference I was talking about.

To me, the significant difference is whether or not we have to apply Einstein's second postulate.

My favorite way to measure the length of a moving meter stick that is going to pass locally by me is to measure its speed with radar Doppler and then time how long it takes to pass by me but even this assumes Einstein's second postulate. I'm not denying that there are ways to measure Length Contraction, only that it requires an application of Einstein's second postulate along with measurements and calculations (or equivalent).

 

[PeterDonis]

The meter sticks must be passing at some distance from the observers (and their cameras) which means that there will be light delay times that must be taken into consideration. I assume that this is what you had in mind.

Yes, but that's true whether the meter stick is moving or not. There is always some amount of approximation involved. But, in a general curved spacetime where the size of a local inertial frame is limited, there is a big difference between measurements that can be made entirely within a single local inertial frame (which, bear in mind, means local in space and time) and measurements which can't. In the latter type of measurement, it's not just a matter of correcting for light delay time; it's a matter of the correction not being unique (because there is no unique way to transport vectors from one event to another in a general curved spacetime). Within a local inertial frame, the correction is unique.

In order to get the correct image that shows the Length Contraction of the moving meter stick as measured by the stationary meter stick, we must fire the strobe at just one instant in relation to the moving meter stick such that the images of the ends of the moving meter stick are equidistant from the images of the ends of the stationary meter stick. If the strobe is fired earlier than that, the image of the moving meter stick will be too short and if it is fired later, the image of the moving meter stick will be too long, agreed?

I agree that you have to fire the strobe at a particular instant, such that the light from the strobe hits each end of the moving meter stick at events that are simultaneous in the frame of the stationary meter stick. (This may be what you were saying, but you worded it differently so I'm not sure.) However, I don't see any real difficulty with setting this up. For example, you could measure the velocity of the moving meter stick (using Doppler), and use that, plus the exact location of the strobe along the stationary meter stick, to determine when to fire the strobe, relative to the instant that the front end of the moving meter stick passes the end of the stationary meter stick, in order to have the strobe light signals hit the meter sticks at the right instant.

let's make it clear that we have also applied Einstein's second postulate to synchronize our stop clocks before hand.

Yes, agreed.

We do have to assume that the light travels in a straight from the ends of the objects to our eyes but we don't care even if the speed is constant, correct?

Yes, we do care that its speed is constant; otherwise we don't know the relationship in time between the images we get from different parts of the objects. For example, in the meter stick example, if the speed of light isn't constant, we don't know how to determine the right instant to fire the strobe.

Would you consider it cheating if we applied the standard of the length of a meter using a cesium clock to count out a specific number of cycles to time how long it takes for light to travel one meter?

No. I am assuming that we have a reliable local method of determining our unit of length that gives the same answer in any local inertial frame. The cesium clock method counts as such a reliable local method.

 

[ghwellsjr]

We do have to assume that the light travels in a straight [line] from the ends of the objects to our eyes but we don't care even if the speed is constant, correct?

Yes, we do care that its speed is constant; otherwise we don't know the relationship in time between the images we get from different parts of the objects. For example, in the meter stick example, if the speed of light isn't constant, we don't know how to determine the right instant to fire the strobe.

I was commenting on your comment with regard to two stationary meter sticks:

One could always say that these measurements are not "direct" because they involve some kind of calculation or assumption; but you could say the same thing about laying the two meter sticks side by side if both were stationary--you have to assume that the light propagating from the sticks to your eyes behaves in a certain way, so that it's giving you accurate information about how the sticks are positioned spatially. In principle, no measurement is ever "direct" in a pure sense; there are always intervening variables and assumptions.

I don't understand why you think it matters when we fire the strobe or why we have to assume that the speed of light is constant in this specific instance.

Please explain.

 

[PeterDonis]

Please explain.

I didn't realize you were talking about the case of stationary meter sticks. Yes, in that case it doesn't matter when you fire the strobe. However, I still think it matters that the speed of light is constant. Strictly speaking, I guess you could say that the speed of light could vary with time without affecting the result; but it can't vary in space, because the paths of the light beams coming from the two ends of the meter sticks are traversing different positions in space. However, variation in time without variation in space in a particular inertial frame would either become partly variation in space in any other frame, or would violate Lorentz invariance; so really I think the assumption of a constant speed of light is necessary for the stationary case as well.

 

[ghwellsjr]

I didn't realize you were talking about the case of stationary meter sticks. Yes, in that case it doesn't matter when you fire the strobe. However, I still think it matters that the speed of light is constant. Strictly speaking, I guess you could say that the speed of light could vary with time without affecting the result; but it can't vary in space, because the paths of the light beams coming from the two ends of the meter sticks are traversing different positions in space. However, variation in time without variation in space in a particular inertial frame would either become partly variation in space in any other frame, or would violate Lorentz invariance; so really I think the assumption of a constant speed of light is necessary for the stationary case as well.

Well, I was speaking strictly and I did say that the light had to travel in a straight line. (I unfortunately left out the word "line" which I have since inserted.)

But the main point I want to make is that strictly for the stationary case, that is, the observer taking a picture of two side-by-side meter sticks that are not moving with respect to him and just a few meters in front of him, or just looking with his eyes, using a strobe light or constant lighting, it is not necessary to invoke Einstein's second postulate to make what you wanted to distinguish as a "direct" length comparison unlike the case of one moving and one stationary meter stick where it is necessary to invoke Einstein's second postulate. I realize that there are other reasons to assume the speed of light is constant and the same in all directions but not strictly for this specific case. Agreed?

 

[Taragond]

Wow...that was a lot...I am not sure I got it all, but I think a question I posted last time (unfortunately hidden between some rambling that may have bored you. If that is the case I apologize. I know how frustrating it can be if you thought you were done with one thing :D) was aimed at a different approach on the same problem, depending your answer on this:

At last, the scenarios measuring a meter-stick got me thinking. What if the meter-stick would instead be a sqare of 1m²? Wouldn't that be a possibility to measure it? Or am I wrong in assuming the reduction in length would only occur parallel to the movement?

Because if so, it should be possible by ataching a perfectly square lightsource and a wide-field-camera to each observers side to automatically measure the "length" by comparing the height of said light-source with it's width corrected for the perspective calculated by it's y-coordinate in the picture. Of course given the paths of the vessels are parallel, or the trajectory of each is known bei both (the measuring one(s)). But I guess if the first part is plausible, there wouldn't be very many positioning lights necessary to automatically calculate that, too...

 

[ghwellsjr]

Wow...that was a lot...I am not sure I got it all, but I think a question I posted last time (unfortunately hidden between some rambling that may have bored you. If that is the case I apologize. I know how frustrating it can be if you thought you were done with one thing :D) was aimed at a different approach on the same problem, depending your answer on this:

At last, the scenarios measuring a meter-stick got me thinking. What if the meter-stick would instead be a sqare of 1m²? Wouldn't that be a possibility to measure it? Or am I wrong in assuming the reduction in length would only occur parallel to the movement?

Because if so, it should be possible by ataching a perfectly square lightsource and a wide-field-camera to each observers side to automatically measure the "length" by comparing the height of said light-source with it's width corrected for the perspective calculated by it's y-coordinate in the picture. Of course given the paths of the vessels are parallel, or the trajectory of each is known bei both (the measuring one(s)). But I guess if the first part is plausible, there wouldn't be very many positioning lights necessary to automatically calculate that, too...

Your question didn't bore me, it just takes time to prepare answers and I spent a lot of time on PeterDonis's issue that a strobe light could be used to measure Length Contraction.

If you understand what Length Contraction is, you will quit asking questions about how to directly observe it. Length Contraction is the ratio of the length of an object as defined according to an Inertial Reference Frame in which the object is moving inertially compared to the length of the object as defined according to the IRF in which the object is at rest. Key to understanding this is that the length of the object according to any IRF is defined as the difference in the spatial coordinates of the object's endpoints (or any other points on the object) that are determined at the same Coordinate Time. Since coordinates are not observable (they can change when we use different IRF's), Length Contraction also cannot be observable. Or to put it another way, different IRF's do not change anything that is observable. What makes the difference between different IRF's is how the propagation of light is defined in them. Remember that the propagation of light is also not observable. Einstein's second postulate is what defines the propagation of light in any IRF. So it takes the application of Einstein's second postulate to a set of observed measurements to establish Length Contraction.

This application will require a measurement involving a roundtrip propagation of light (or radar) signals, from the observer to the object and back to the observer. That is why PeterDonis used a strobe light. In your suggested scenario, you only have a one-way propagation of light from the illuminated square to the wide-field camera so that cannot fulfill the requirement that the dimensions of the object be taken at the same Coordinate Time. You should also realize that nothing is actually happening to an object when we use different IRF's. It's just our description of it that changes.

Does this help?

 

[PeterDonis]

I realize that there are other reasons to assume the speed of light is constant and the same in all directions but not strictly for this specific case. Agreed?

No. The light reaching your eyes at the same time from the two ends of the meter sticks still has to have left the two ends of the meter sticks at the same time; otherwise you are not seeing a "snapshot" of the two sticks at a single instant of time, so you can't interpret what you see as a "length" at all. But Einstein's second postulate is required to ensure that the light reaching your eyes at the same time, if the distances are the same, left the two ends of the meter sticks at the same time.

(To put it another way, if Einstein's second postulate did not hold, you could have an effect similar to Penrose-Terrell rotation even for objects that were stationary relative to you, so even a stationary length comparison--or even a stationary length measurement of a single meter stick--would not be "direct" by your definition, because you would have to correct for different light travel times from different parts of the object.)

 

[ghwellsjr]

No. The light reaching your eyes at the same time from the two ends of the meter sticks still has to have left the two ends of the meter sticks at the same time; otherwise you are not seeing a "snapshot" of the two sticks at a single instant of time, so you can't interpret what you see as a "length" at all. But Einstein's second postulate is required to ensure that the light reaching your eyes at the same time, if the distances are the same, left the two ends of the meter sticks at the same time.

(To put it another way, if Einstein's second postulate did not hold, you could have an effect similar to Penrose-Terrell rotation even for objects that were stationary relative to you, so even a stationary length comparison--or even a stationary length measurement of a single meter stick--would not be "direct" by your definition, because you would have to correct for different light travel times from different parts of the object.)

How does that comport with Einstein's comments from chapter 2 of his 1920 book on relativity:

"ON the basis of the physical interpretation of distance which has been indicated, we are also in a position to establish the distance between two points on a rigid body by means of measurements. For this purpose we require a “distance” (rod S) which is to be used once and for all, and which we employ as a standard measure. If, now, A and B are two points on a rigid body, we can construct the line joining them according to the rules of geometry; then, starting from A, we can mark off the distance S time after time until we reach B. The number of these operations required is the numerical measure of the distance AB. This is the basis of all measurement of length."

 

[PeterDonis]

How does that comport with Einstein's comments

He describes the distance measurement as "marking off", which is not quite the same as what we've been discussing. To compare the lengths of two meter sticks by his method, you would place them together so that they were flush at one end, and verify that by observation--but that observation only involves one end of each stick, so the issue I described doesn't arise. Then you would hold both sticks in place by some method and move to the other end of the "standard" meter stick and see where it fell on the stick you wanted to measure, and make a mark on the stick being measured accordingly. In the case we've been discussing, you could leave out the mark, because the other end of the stick being measured would also be flush with the other end of the standard stick; but if, for example, the stick being measured were two meters long, you would make a mark on it where the end of the standard stick fell. Then you would move the standard stick until its other end was at the mark you just made, verify that by observation, and then move to the other end of the standard stick again, holding both objects in place, to see where it fell on the stick being measured. But in any case, you would be observing only one end at a time, so the issue I described would not arise.

The issues that would arise are, first, how you guarantee that both sticks are in fact held exactly in place while you move from one end to the other of the standard stick, and second, how you guarantee that the standard stick's length is unchanged after you have moved it.

 

[Taragond]

Your question didn't bore me, it just takes time to prepare answers

That I understand perfectly well! I just wanted to make sure because we're still on the internet, even though I already was pretty sure, it's "rules" don't apply here ;)
Also because of my little expertise on discussing physics I am aware that my questions and statements could be stupid from your point of knowledge and how hard it is to point that out and still have me learn something to correct that...

Length Contraction also cannot be observable. Or to put it another way, different IRF's do not change anything that is observable.

Does this help?

I'm not sure, because I always understood it that way, a rocket would look shorter to us on it's passing, than it actually is. Actually I'm pretty sure that exactly was explained to me in school but maybe there is something missing now. That's why I had the presumption it was observable.
But If I know understand you correctly:

lets say wie have a stationary camera and the suare is dark but flashes over it's entire front just one photon-burst at precisely the same time towards the camera when passing by.
Assuming it is strong enough so the camera can detect them, it would still see a square in the picture?

 

[ghwellsjr]

Length Contraction also cannot be observable. Or to put it another way, different IRF's do not change anything that is observable.

Does this help?

I'm not sure, because I always understood it that way, a rocket would look shorter to us on it's passing, than it actually is. Actually I'm pretty sure that exactly was explained to me in school but maybe there is something missing now. That's why I had the presumption it was observable.
But If I know understand you correctly:

lets say wie have a stationary camera and the suare is dark but flashes over it's entire front just one photon-burst at precisely the same time towards the camera when passing by.
Assuming it is strong enough so the camera can detect them, it would still see a square in the picture?

No, it would not be a square but I think you are still missing my point. When I said that different IRF's do not change anything that is observable, I didn't mean that something that looks like a square to an observer (or a camera) at rest with respect to it would also look like a square to an observer (or a camera) moving with respect to it. What I meant was that however a moving object appears to an observer (or a camera) as analyzed according to one IRF, will continue to show that the object appears the same to that observer (or camera) according to any other IRF.

So let's analyze your scenario to see what a moving square that simultaneously gives off a flash of light looks like to a stationary camera. I'm assuming you meant "at precisely the same time" in the rest frame of the square. Let's use a pinhole camera with a flat film. To make things especially easy for us to analyze, let's make the distance between the film and the pinhole be the same as the distance between the pinhole and the moving square at its closest approach. That means that whatever the positions of the photons according to the rest frame of the camera but in the plane of the moving square when they are emitted will be similar to the positions of the photons in the plane of the stationary film when they are detected. (I hope that makes sense to you.) So all we have to do is determine what the shape of the illumination is in the camera's rest frame without regard to when those photons were emitted. To do that, we start with the rest frame of the square and transform that to the rest frame of the camera. I'm going to assume a square of 1 meter on each side (10 decimeters) and look at a slice along the direction of motion at 0.6c. Here is a spacetime diagram showing the square in its rest frame. Assume the flash occurs at the Coordinate Time of zero, which is the bottom dots on both worldlines:

Now we transform to the rest frame of the camera where the square is moving at 0.6c:

If we look at the Coordinate Time of 10, we see that the length is contracted to 8 decimeters. Since gamma at 0.6c is 1.25, this is in agreement with 10 decimeters divided by 1.25. However, what is important for our scenario is the relative positions of the flashes at the two ends of the square which you will remember are the bottom two dots and these are separated by 12.5 decimeters. So the image that will be recorded on the film is not a square of 10 decimeters on a side but rather a rectangle that is 10 decimeters high and 12.5 decimeters wide. It won't matter what other IRF we transform this scenario to, they all will show an image of a stretched out square rather than a contracted square.