Understanding Frames of Reference in Relativity

[H0T_S0UP]

I'm not going lie I don't know too much about relativity, though I do understand it. I haven't even gone to college yet and from what I've read so far I'm assuming there's much more to know. Anyway, in most of Einsteins thought experiments he speaks about observations in terms of 1 frame of reference. They lead to paradoxes such as time dilation and the increasing/decreasing 'rate' of time. This leads to the conclusion that since each perception is different in its respective frame of reference, all frames of reference are valid. But why is human perception taken into account in the first place? I mean our perception distorts everything. We can't even be sure if everything we are thinking is 100% wrong.

Wouldn't it be more accurate to look at events in terms of how the events are happening rather than how the events are happening with respect to something else? What i mean is wouldn't using only one frame of reference be invalid, there by invalidating all frames of reference, and instead using two equal frames of reference simultaneously under similar conditions? This would create a frame of reference that that uses two different FoR's at the same time to cancel out individual perception and prove that is it possible to do something such as (like Einstein said) synchronize all clocks in a town equally.

Damn I think I just confused myself stating all that. I should probably read more on relativity. Also sometime I find it hard to put my thoughts into words, its a type of 3 dimensional thinking I believe, or so I was told.

 

[JesseM]

I'm not going lie I don't know too much about relativity, though I do understand it. I haven't even gone to college yet and from what I've read so far I'm assuming there's much more to know. Anyway, in most of Einsteins thought experiments he speaks about observations in terms of 1 frame of reference.

What specific thought experiments are you talking about? Most of the thought experiments I have seen involve a comparison of the same situation viewed from two different frames of reference.

 

[H0T_S0UP]

I recall reading about a thought experiment where an observer was placed between two bolts of lightning. At first the observer was not moving confirming that the bolts hit the ground simultaneously. Now the observer is moving toward one bolt, according to Einstein the lighting bolts would no longer have hit the ground the same time (with respect to the observer) because of the Doppler effect. I understand that the bolts did not hit the ground at the same time according to the moving observer but I don't understand why the point would even be valid when in reality the bolts hit the ground at the same time. Get what I'm saying now. Wouldn't it make more sense to distinguish perception from reality rather than integrate them as relativity does?

Let me put it this way: What would happen if were to to make a frame of reference that look at everything that is occurring in the universe all at once? Wouldn't we see some type of synchronization or pattern if everything was look at with respect to everything else?

 

[JesseM]

I recall reading about a thought experiment where an observer was placed between two bolts of lightning. At first the observer was not moving confirming that the bolts hit the ground simultaneously. Now the observer is moving toward one bolt, according to Einstein the lighting bolts would no longer have hit the ground the same time (with respect to the observer) because of the Doppler effect.

Actually the whole idea of this thought experiment is to consider the same lightning strikes from the perspective of two observers, one who's on a train moving with respect to the ground, and one who's at rest relative to the ground. And it has nothing to do with the Doppler effect, rather it's based on the idea that each observer assumes that light moves at the same speed c in their own rest frame, which means that if the observer on the ground says the lightning bolts hit either end of the train car simultaneously, then the observer on the train car must say that one bolt hit before the other. Here's a summary of this thought-experiment from the textbook https://www.amazon.com/dp/0716723271/?tag=pfamazon01-20:

The Principle of Relativity directly predicts effects that initially seem strange--even weird. Strange or not, weird or not; logical argument demonstrates them and experiment verifies them. One effect has to do with simultaneity: Let two events occur separated in space along the direction of relative motion between laboratory and rocket frames. These two events, even if simultaneous as measured by one observer, cannot be simultaneous as measured by both observers.

Einstein demonstrated the relativity of simultaneity with his famous Train Paradox. (When Einstein developed the theory of special relativity, the train was the fastest common carrier.) Lightning strikes the front and back ends of a rapidly moving train, leaving char marks on the train and on the track and emitting flashes of light that travel forward and backward along the train (Figure 3-1). An observer standing on the ground halfway between the two char marks on the track receives the two light flashes at the same time. He therefore concludes that the two lightning bolts struck the track at the same time--with respect to him they fell simultaneously.

A second observer rides in the middle of the train. From the viewpoint of the observer on the ground, the train observer moves toward the flash coming from the front of the train and moves away from the flash coming from the rear. Therefore the train observre receives the flash from the front of the train first.

This is just what the train observer finds: The flash from the front of the train arrives at her position first, the flash from the rear of the train arrives later. But she can verify that she stands equidistant from the front and rear of the train, where she sees char marks left by the lightning. Moreover, using the Principle of Relativity, she knows that the speed of light has the same value in her train frame as for the ground observer (Sectin 3.3 and Box 3-2), and is the same for light traveling in both directions in her frame. Therefore the arrival of the flash first from the front of the train leads her to conclude that the lightning fell first on the front end of the train. For her the lightning bolts did not fall simultaneously. (To allow the train observer to make only measurements with respect to the train, forcing her to ignore Earth, let the train be a cylinder without windows--in other words a spaceship!)

Did the two lightning bolts strike the front and the back of the train simultaneously? Or did they strike at different times? Decide!

Strange as it seems, there is no unique answer to this question. For the situation described above, the two events are simultaneous as measured in the Earth frame; they are not simultaneous as measured in the train frame. We say that the simultaneity of events is, in general, relative, different for different frames. Only in the special case of two or more events that occur at the same point (or in a plane perpendicular to the line of relative motion at that point--see Section 3.6) does simultaneity in the laboratory frame mean simultaneity in the rocket frame. When the events occur at different locations along the direction of relative motion, they cannot be simultaneous in both frames. This conclusion is called the relativity of simultaneity.

The relativity of simultaneity is a difficult concept to understand. Almost without exception, every puzzle and apparent paradox used to "disprove" the theory of relativity hinges on some misconception about the relativity of simultaneity.

I understand that the bolts did not hit the ground at the same time according to the moving observer but I don't understand why the point would even be valid when in reality the bolts hit the ground at the same time.

Why do you think the "reality" is that the bolts hit the ground at the same time? The thought experiment simply says that if each observer assumes that light moves at c in their own rest frame, then the observer on the ground concludes they hit at the same time (because the light from each strike reaches him at the same moment, and both strikes occurred an equal distance from his position according to his ruler) while the observer on the train concludes they hit at different times (because the light from each strike reaches him at different moments, and both strikes occurred an equal distance from his position according to his ruler). There is no physical basis for thinking one perspective is more true than the other.

 

[H0T_S0UP]

Why do you think the "reality" is that the bolts hit the ground at the same time?

Its tough to explain, if I were to use a frame of reference with an observer 1 mile from the train relativity would still hold true regarding which lightning bolt hit first. What I'm trying to find is a way to take human perception out of the equation to determine that the lightning bolts did factually hit at the same time.

 

[matheinste]

Hello HOT SOUP.

Don't take the word observer too literally. It does not have to be a human observer, it might just as well be a light detector or any relevant apparatus.

Matheinste

 

[Antenna Guy]

Its tough to explain, if I were to use a frame of reference with an observer 1 mile from the train relativity would still hold true regarding which lightning bolt hit first. What I'm trying to find is a way to take human perception out of the equation to determine that the lightning bolts did factually hit at the same time.

Well... JesseM has already claimed that Doppler effects have nothing to do with this thought experiment, but I have yet to see anyone prove that the light coming from either end of the train is the same color in both frames.

Regards,

Bill

 

[H0T_S0UP]

Hello HOT SOUP.

Don't take the word observer too literally. It does not have to be a human observer, it might just as well be a light detector or any relevant apparatus.

Matheinste

I was unaware of that, looks like I got to do some more reading. This is very intriguing if these laws hold true for inanimate objects as well. I really do love this kind of stuff but have to be in the mood to look into it most of the time. I've got a few ideas that I am saving for my first year at college. Then again I'm probably not the only one.

 

[matheinste]

Hello HOT SOUP

Physics, and so relativity, is all about measurement and inanimate appparatus is usually more trustworthy and more accurate than human senses at measuring things.

Matheinste.

 

[JesseM]

Well... JesseM has already claimed that Doppler effects have nothing to do with this thought experiment, but I have yet to see anyone prove that the light coming from either end of the train is the same color in both frames.

I didn't mean that the light would be the same color in both frames, I just meant that the Doppler effect has nothing to do with the fact that different observers disagree about simultaneity, which is the point of that particular thought experiment.

 

[MeJennifer]

Note that actual measurements in relativity scenarios are not what many talk about when they talk about what is observed. What is observed is often not what is actually measured! Bondi k-calculus is what should be used to determine and understand what is actually measured instead of imagining some plane of simultaneity that has a zero physical relevance. Probably 80% of all the misunderstandings in relativity is due to the fact that measured and observed data is not identical.

 

[Antenna Guy]

What is observed is often not what is actually measured!

I assume you agree that color (frequency) can be measured.

Regards,

Bill

 

[JesseM]

Its tough to explain, if I were to use a frame of reference with an observer 1 mile from the train relativity would still hold true regarding which lightning bolt hit first. What I'm trying to find is a way to take human perception out of the equation to determine that the lightning bolts did factually hit at the same time.

The coordinates an observer assigns to events in his frame of reference has nothing at all to do with where he is located, only how he is moving relative to other objects. If you had one observer at the position of the middle of the train when the lightning struck, another 1 mile away, another 100 light-years away, then as long as all these observers are at rest with respect to one another they will all agree about whether or not the strikes were simultaneous.

As I said, one way of dealing with light signal delays is just to factor out the time the light would take to get to you based on the distance of the event and the assumption that light moves at c in your frame. Another would be to use a network of rulers and clocks at rest relative to you, with the clocks "synchronized" using the assumption light moves at c in your frame (the Einstein clock synchronization convention) and only assign times to events based on clocks that were right next to the events as they happened. I discussed this with another poster on an older thread you might want to take a look at.

 

[H0T_S0UP]

Here's another relativity question. Suppose a 2 foot long rod is placed inside a gun when it is launched it will fire near the speed of light, c. Before the rod is launched it is measured in a motionless state. When the rod is launched it travels down a tunnel which has two high speed cameras watching the projectile. The first one moves with the rod and the other remains motionless. As the rod travels past the motionless camera, would the picture it takes of the rod be smaller than its actual size and if so by how much? for the moving camera, would the shot be distored because of both speed and time dilation (say there is counter imposed on the camera's screen as it films the rod fly past/with it).

 

[JesseM]

Here's another relativity question. Suppose a 2 foot long rod is placed inside a gun when it is launched it will fire near the speed of light, c. Before the rod is launched it is measured in a motionless state. When the rod is launched it travels down a tunnel which has two high speed cameras watching the projectile. The first one moves with the rod and the other remains motionless. As the rod travels past the motionless camera, would the picture it takes of the rod be smaller than its actual size and if so by how much? for the moving camera, would the shot be distored because of both speed and time dilation (say there is counter imposed on the camera's screen as it films the rod fly past/with it).

Again you have to distinguish between what you see visually and what is true in your frame. If the rod is moving at 0.6c in your frame, and you have two clocks which are 1.6 feet apart and at rest in your frame, and the clocks have been synchronized in your frame according to the Einstein synchronization procedure, then the reading on one clock as the back end of the rod is passing it will be the same as the reading on the other clock as the front end is passing it, so in your frame the events of each end being next to each clock were simultaneous, so the rod is 1.6 feet long in your frame. But visually it won't appear to be 1.6 feet long, because you have to take into account that light from the far end of the rod takes longer than light from the near end to reach your eyes, so this visually distorts the length to make it appear longer than it "really" is in your frame, which means that, as explained on this thread, it would actually appear to be the same length as it was when at rest (2 feet in this case), though its appearance would be distorted in other ways. This is known as the Penrose-Terrell effect, but note that it's purely about the appearance of moving objects rather than their length and shape as measured using simultaneous events at different points on the object (like its two ends passing synchronized clocks which both read the same time).

 

[H0T_S0UP]

So the objects under relativity go under apparent changes as they approach the speed of light. The rod moving at near C wouldn't actually contract, but it would appear to since light takes time to reach an observer. If what I'm saying is correct then this is much more clear to me now. If not then I'm a very lost soul searching for relativity in a lonely world...ha!

 

[JesseM]

So the objects under relativity go under apparent changes as they approach the speed of light. The rod moving at near C wouldn't actually contract, but it would appear to since light takes time to reach an observer.

No, you've got it backwards, it wouldn't appear to contract because light takes time to reach an observer, even though it "really" would have contracted in your frame. Like I said, if its rest length was 2 ft, then if it's moving at 0.6c in your frame, then its "real" length in your frame would be 1.6 ft because of Lorentz contraction, but visually it would still appear to be 2 ft long because of the Penrose-Terrell effect.

 

[H0T_S0UP]

Ok I think I understand now. I only took a physics course in high school and I'm just starting college this year so most of this is new to me. Let me ask this: Why would an object contract as approaches the speed of light. What force is it undergoing that causes it to change its shape?

 

[JesseM]

Ok I think I understand now. I only took a physics course in high school and I'm just starting college this year so most of this is new to me. Let me ask this: Why would an object contract as approaches the speed of light. What force is it undergoing that causes it to change its shape?

There aren't any forces changing its shape, and the shape-change isn't really objective--in my frame your ruler is shrunk relative to mine, but in your frame my ruler is shrunk relative to yours, there's no physical way to determine a truth about whose ruler is "really" shorter.

 

[H0T_S0UP]

Ok let's verify this one last time. If this 2 foot rod was to launch past me at .75c and I was just standing still, it would decrease in volume but because of the speed that light travels it would appear to retain its motionless volume. Time for the rod would slow down since it is moving so fast. All of this is only relative to my frame so if I was .375c all these properties would change.

 

[yuiop]

So the objects under relativity go under apparent changes as they approach the speed of light. The rod moving at near C wouldn't actually contract, but it would appear to since light takes time to reach an observer. If what I'm saying is correct then this is much more clear to me now. If not then I'm a very lost soul searching for relativity in a lonely world...ha!

Hi Soup,

Please don't let the Penrose-Terell effect confuse you! It should never be introduced to beginners for that reason. Length contraction is nothing to do with light travel times and is more real than a mere optical illusion. What should be made very clear to all beginners in SR is that light travel times are always allowed for and deducted and we are only looking at the residual effects when looking at time dilation and length contraction. A better way to measure the length of the moving rod would be to have a row of ink jets simultaneously spray a short blast of ink at the rod as it passes and observe the silhouette of the rod left by the ink on a wall behind the rod.

 

[JesseM]

Ok let's verify this one last time. If this 2 foot rod was to launch past me at .75c and I was just standing still, it would decrease in volume but because of the speed that light travels it would appear to retain its motionless volume.

It would decrease in length in your frame, although not in its own frame--length contraction is always frame-dependent. And yes, despite the fact that its length is shorter in your frame, its length will look unchanged to you visually because of the Penrose-Terrell effect.

Time for the rod would slow down since it is moving so fast.

It's only moving fast relative to you, there is no objective notion of speed in relativity. In the rod's own rest frame, its speed is zero while you are the one moving fast, so in its frame your clock would be the one running slow.

All of this is only relative to my frame so if I was .375c all these properties would change.

0.375c relative to what? Again, you can't talk about an object's speed in any objective sense, only relative to some other object.

 

[H0T_S0UP]

sorry I should have been more specific. By that last sentence I meant that everything I was speaking about is strictly relative between me and the rod.

 

[JesseM]

sorry I should have been more specific. By that last sentence I meant that everything I was speaking about is strictly relative between me and the rod.

OK, then in your frame the rod is measured to be shorter, and a clock attached to the rod is measured to be running slow relative to your own, but visually things are a little different thanks to light delays--because of the Penrose-Terrell effect the length of the rod will look unchanged, and because of the Doppler effect, if the rod is moving towards you its clock will look like its sped up rather than slowed down (and if it's moving away from you the clock will look like it's ticking even slower than the amount you measure it to be ticking in your frame).

 

[MeJennifer]

OK, then in your frame the rod is measured to be shorter, and a clock attached to the rod is measured to be running slow relative to your own, but visually things are a little different thanks to light delays--because of the Penrose-Terrell effect the length of the rod will look unchanged, and because of the Doppler effect, if the rod is moving towards you its clock will look like its sped up rather than slowed down (and if it's moving away from you the clock will look like it's ticking even slower than the amount you measure it to be ticking in your frame).

So it is measured to be shorter but visually it is not? That does not make any sense.
You probably meant to write observed to be shorter.

 

[rbj]

No, you've got it backwards, it wouldn't appear to contract because light takes time to reach an observer, even though it "really" would have contracted in your frame. Like I said, if its rest length was 2 ft, then if it's moving at 0.6c in your frame, then its "real" length in your frame would be 1.6 ft because of Lorentz contraction, but visually it would still appear to be 2 ft long because of the Penrose-Terrell effect.

now I'm confused. you are saying that the Penrose-Terrell effect means that length-contracted rods do not appear length-contracted??

i thought the whole point of length contraction in SR is that a rod moving in the same direction as its orientation (along the long dimension of the rod) at relativistic speeds relative to some observer appears shorter to that observer than it would to an observer who was moving along with the rod (to whom the rod appears stationary).

 

[JesseM]

So it is measured to be shorter but visually it is not? That does not make any sense.
You probably meant to write observed to be shorter.

"Measured" and "observed" are usually synonymous in SR, I think. The measurement would involve the standard notion of a network of rigid rulers and clocks all sharing the same inertial rest frame and with the clocks synchronized according to the Einstein synchronization convention, with events assigned coordinates based solely on local readings in this system. So, for example, if a rod is moving relative to my network of rulers and clocks, and at the moment the back end of the rod passes the 15-meter mark on my x-axis ruler, the clock at the 15-meter mark reads a time of 12 seconds, then I say that at t=12 seconds in my frame the back end of the rod was at position x=15 meters. Likewise, if at the moment the front end of the rod passes the 10-meter mark on my x-axis ruler, the clock at the 10-meter mark reads a time of 12 seconds, then I say that at t=12 seconds in my frame the front end of the rod was at position x=10 meters. Are these not measurements? And since these measurements are simultaneous in my frame, that must mean that in my frame the rod is measured to be 15-10 = 5 meters long.

 

[JesseM]

now I'm confused. you are saying that the Penrose-Terrell effect means that length-contracted rods do not appear length-contracted??

Visually, no they don't appear to be contracted, although they appear distorted in other ways. See this thread.

i thought the whole point of length contraction in SR is that a rod moving in the same direction as its orientation (along the long dimension of the rod) at relativistic speeds relative to some observer appears shorter to that observer than it would to an observer who was moving along with the rod (to whom the rod appears stationary).

This is a common misunderstanding--length contraction and time dilation are not based on visual perceptions, rather they are based on coordinates assigned to events which factor out the problem of light delays, either by backdating every perceived event based on its distance and the assumption that the light from the event to you was moving at c in your frame (so if I see an event 10 light-seconds away when my clock reads t=30 seconds, I'll assign the event a time-coordinate of t=20 seconds in my frame), or more commonly by assuming that all measurements are local ones made on the type of grid of rulers and clocks I talked about in my last post to MeJennifer. See this thread for more on the importance of factoring out light delays in SR.

 

[MeJennifer]

Perhaps Jesse, we should specifically request if any of the statements you make on this forum pertain to physical measurements done by scientific instruments (or is that still too vague for you?) or that they are just inferences by imagining a plane of simultaneity?

In the past you have made a clear distinction between what is measured and what is observed now you seem to be backtracking from that, or is it perhaps that you have trouble admitting that you are wrong once in a while?

 

[JesseM]

Perhaps Jesse, we should specifically request if any of the statements you make on this forum pertain to physical measurements done by scientific instruments (or is that still too vague for you?) or that they are just inferences by imagining a plane of simultaneity?

What, local measurements on actual physical clocks are not "physical measurements done by scientific instruments"? Of course the resulting length measurement is frame-dependent (and dependent on using the Einstein synchronization convention to synchronize the clocks), but it's still a type of "measurement" as I would understand the term.

In the past you have made a clear distinction between what is measured and what is observed

Really? What specific post are you thinking of? Anyway, this is just semantic quibbling on your part, I think it is standard to define "measurement" as synonymous with "observation" in SR, but if you choose to reserve "measurement" solely for frame-independent quantities, no one is going to stop you, as long as you spell out your definition and don't play gotcha games of saying people are wrong for using the term differently (unless you can show that your usage is the standard accepted one among physicists).

now you seem to be backtracking from that, or is it perhaps that you have trouble admitting that you are wrong once in a while?

That's pretty rich coming from you, who has made all sorts of silly claims that you simply stopped discussing after I pressed you on them and pointed to statements from mainstream physicists that contradicted them, like the claim that black holes can't form in closed universes, or the claim that there is a single "true" distance between two objects defined (in some manner you refused to actually spell out) by light travel time.

 

[H0T_S0UP]

Ok about this length contraction, what is actually happening to the rod that causes it to lose volume (relative to my frame)? If I were to run past the rod at twice its speed after I just watched the rod zoom past me when I was motionless would I see an increase in size?

 

[JesseM]

Ok about this length contraction, what is actually happening to the rod that causes it to lose volume (relative to my frame)? If I were to run past the rod at twice its speed after I just watched the rod zoom past me when I was motionless would I see an increase in size?

Again, all motion is relative motion. As long as you are moving inertially, it is always possible to find an inertial frame where you are at rest, and in this frame it will always be other objects in motion relative to you that are shrunk relative to you. Nothing ever expands to a length greater than its rest length in any inertial frame.

 

[paw]

Ok about this length contraction, what is actually happening to the rod that causes it to lose volume (relative to my frame)? If I were to run past the rod at twice its speed after I just watched the rod zoom past me when I was motionless would I see an increase in size?

Try thinking of it this way. Nothing is really happening to the rod. No forces are acting on it. It's not being crushed or anything like that.

What is changing is the result you get when you measure it. If the rod goes past you at some speed v you will measure the rod to be shorter than if it was stationary from your point of view. If someone was riding on the rod they won't see the rod change in any way .

Now if you accelerate and pass the rod so it appears to have reversed direction and is now traveling some other speed, say -2v from your new frame of reference, the rod appears even shorter than it did before when it appeared to be doing speed v. Notice the direction doesn't matter, just the relative speed.

Say you now slow down and let the rod catch up with you then match speed with it. From your original frame both you and the rod are now traveling at v but it is easier to define a new frame where both you and the rod are not moving. In this case you measure the rod to be the same as its original length which is exactly what you'd expect.

The reason this works is there's no way to decide whether you, the rod or both are moving in any absolute sense. Because of this we are free to use whatever inertial frame (point of view) we want.

So it's all in how you look at it, from what frame of reference you are measuring the rod. This doesn't make length contraction any less real. It is a real effect. But hopefully this will help you understand that nothing is really happening to the rod.

 

[MeJennifer]

Try thinking of it this way. Nothing is really happening to the rod. No forces are acting on it. It's not being crushed or anything like that.

That is correct.

All that is happening is that some people want to "explain" relativity by creating 3-planes of simultaneity that gives an enormous source of confusion. Such 3-planes are simply mental constructs as there is nothing physical about them.

A far better description of what is really happening, e.g what is actually measured instead of inferred by such measurements is to use Bondi k-calculus.

 

[Antenna Guy]

All that is happening is that some people want to "explain" relativity by creating 3-planes of simultaneity that gives an enormous source of confusion. Such 3-planes are simply mental constructs as there is nothing physical about them.

I never really thought of them as 3-planes, but I can see why you refer to them as such. However confusing they may be, I don't see them as inherently inaccurate if applied appropriately.

A far better description of what is really happening, e.g what is actually measured instead of inferred by such measurements is to use Bondi k-calculus.

I suppose this begs the question of whether an inference made by one technique agrees with calculation based upon another approach to the same problem.

Regards,

Bill