Short question about length contraction

[HALON]

The at rest distance between Betty the astronaut and a flag in open space is $1$ unit. If Betty approaches the flag at constant speed while laying out metre rulers, will she have laid out $1$ unit of at rest rulers when she reaches the flag? Or will the number of rulers laid out exceed $1$ due to length contraction?

 

[Nugatory]

You'll have to specify two more things before we can answer your question.

First, exactly what do you mean by "the rest distance between Betty and the flag"? Betty and the flag are moving relative to one another so the distance between them is constantly changing. I think what you mean is equivalent to: there are two flags, they are at rest relative to another, they are one unit apart according to an observer at rest relative to both flags, and moving Betty starts placing meter sticks as she passes one of the flags moving towards the other.

Second, when Betty places the meter sticks, are they at rest relative to her or relative to the flags after she places them?

 

[HALON]

Yes, I see how it might get tricky. We could say the distance between Betty’s starting point and the flag was pre-determined by radar signal. The flag may be on a planet (but let’s forget gravity) then Betty accelerates from a previous position only until she reaches the starting point where she begins to lay out a ruler, waits until her motion carries her to the end of the ruler, then lays out another ruler and so on. Hmmm, I guess the “laying out” part involves acceleration which makes it complicated. I’m sorry I asked now!

 

[Simon Bridge]

You can see how you have to be very careful with your descriptions in relativity...

We could say the distance between Betty’s starting point and the flag was pre-determined by radar signal. The flag may be on a planet (but let’s forget gravity) then Betty accelerates from a previous position only until she reaches the starting point where she begins to lay out a ruler, ...

Was it pre-determined by a radar signal from a radar range-finder that was stationary wrt the flag, or one that was moving?
This is the most important bit of information.

Do you want the meter sticks to end up stationary wrt the flag when Betty "lays them out"?

Say Betty runs a course that is proper length $D$ meters long, in Betty's frame that would be $D/\gamma$ meters long: length contraction.

Betty drops a marker every one of her meters, starting with one that hits the start line.
The marker hits and sticks to the course and Betty is a perfect shot.
Kinda like a relativistic fence-builder putting in fence posts.

That what you had in mind?

 

[HALON]

Was it pre-determined by a radar signal from a radar range-finder that was stationary wrt the flag, or one that was moving?

Yes, it was stationary wrt the flag. Betty and an observer at the flag agreed beforehand on the distance.

Do you want the meter sticks to end up stationary wrt the flag when Betty "lays them out"?

To end up stationary would involve negative acceleration which would affect the number of markers counted. If she just brushed the flag in passing it might be easier to calculate.

Kinda like a relativistic fence-builder putting in fence posts. That what you had in mind?

I just thought of someone pacing out a distance, originally.

 

[Simon Bridge]

To end up stationary would involve negative acceleration which would affect the number of markers counted. If she just brushed the flag in passing it might be easier to calculate.

Betty could brush the start and finish lines and time how long it takes for them to pass (remember, in Betty's frame, the start and finish are moving!) Betty knows v and has timed t so gets d=v/t ... and finds out that d measured this way is smaller than the d obtained by the radar.

I just thought of someone pacing out a distance, originally.

... sure - so we imagine that Betty is "pacing out" a distance. The faster she goes, the fewer paces it takes to get from the start flag to the finish flag.
OK you'd normally lengthen your stride to go faster, but Betty is ultra-disciplined and always keeps the same pace length as measured by the ruler she is holding at the time.

That better?

Thing is - in each one of your descriptions, you are leaving something out... you kinda trail off.
Like you suggested touching the flag, but not what that was supposed to do; and pacing the distance but not what it was about the paces you wanted to know.
Try making a complete description.

 

[HALON]

I'll try again

 

[HALON]

Touching the flag is the signal for Betty to know when to stop counting paces.

so we imagine that Betty is "pacing out" a distance. The faster she goes, the fewer paces it takes to get from the start flag to the finish flag.

This is the part I wasn't sure about. In a rotation, it is said, it takes more paces to complete a revolution, so this is an interesting difference.

I’ll try to formulate it. First, the gamma factor is
$\gamma=1/(1-(v/c)^2)^{1/2}$

I'll call the distance between two Einstein synchronized points (Betty’s flag and your flag) the rest frame distance, or $d$. So the travel time between her flag and your flag for the rest frame distance is $d=vt$.
In your frame, if $t$ is the time traveled by Betty to your flag, then in Betty’ frame $d_{Betty}=vt(1/γ)$.
To square this up with your distance we get $d_{Betty}=d_{Simon}(1/γ)$
From the previous relation we see Betty's distance is contracted relative to yours.

 

[ghwellsjr]

Yes, I see how it might get tricky. We could say the distance between Betty’s starting point and the flag was pre-determined by radar signal. The flag may be on a planet (but let’s forget gravity) then Betty accelerates from a previous position only until she reaches the starting point where she begins to lay out a ruler, waits until her motion carries her to the end of the ruler, then lays out another ruler and so on. Hmmm, I guess the “laying out” part involves acceleration which makes it complicated. I’m sorry I asked now!

You had Betty accelerating from a previous position to the "starting" point.

I have a suggestion:

Why don't you make that position far removed from the starting point and why don't you have her remain at rest for awhile there so that she will have time to use radar to measure the distance between the "starting" point and the flag? Then have her accelerate rapidly to her final speed but reach it long before she gets to the "starting" point so that she will have time to use radar to again measure the distance between the "starting" point and the flag. She can also use radar to measure her final speed relative to the "starting" point (and the flag). Then she can measure how long it takes for her to traverse the distance from the "starting" point to the flag and confirm that the distance she traveled matches the distance she determined from radar?

I hope you have given up on the idea of her laying out rulers between the "starting" point and the flag because Special Relativity cannot address that issue as it would require an analysis of the structure of the rulers and how they deform as a result of extreme accelerations. And you would have to tell us exactly the process by which Betty determines when to lay out each next ruler. You might think that it would be obvious but it's not. For example, does she accelerate just one end of each ruler? Which end? How can she be sure that when the acceleration force propagates and dissipates through each ruler, the two ends of each ruler butt up against the adjacent rulers? Then you have to tell us what the final Proper Length of the rulers are after the vibrations dampen out. And that will be the answer to your question of how many rulers are laid out between the "starting" point and the flag.

To reiterate: you have to tell us that answer because Special Relativity can't.

 

[ghwellsjr]

I'll call the distance between two Einstein synchronized points (Betty’s flag and your flag) the rest frame distance, or $d$. So the travel time between her flag and your flag for the rest frame distance is $d=vt$.
In your frame, if $t$ is the time traveled by Betty to your flag, then in Betty’ frame $d_{Betty}=vt(1/γ)$.
To square this up with your distance we get $d_{Betty}=d_{Simon}(1/γ)$
From the previous relation we see Betty's distance is contracted relative to yours.

You keep adding and changing things:

Originally you had one flag and one "starting" point. Now you have two flags called Betty's flag and your flag. Who are you? And which of these new flags corresponds to the original flag? Why don't you just label them starting flag and ending flag or final flag? And now you're talking about different frames. You should define your scenario according to a single frame and show how Betty makes her measurements or does whatever you want her to do. Then you can transform to any other frame and see how the same scenario looks in that new frame but it won't change any observerations, any measurements, any calculations, any conclusions.

 

[HALON]

I hope you have given up on the idea of her laying out rulers between the "starting" point and the flag because Special Relativity cannot address that issue as it would require an analysis of the structure of the rulers and how they deform as a result of extreme accelerations.

It's a tough one, yes. Yet other authors have used the "pacing out" method on spinning disk's to conclude that more of them will fit per revolution than ought to be measured when the speed is close to zero. And that's supposed to be a special relativity problem.

But even if one walks there is acceleration, despite overall speed being uniform, because the feet are planted while the body's momentum does the rest.

 

[ghwellsjr]

It's a tough one, yes. Yet other authors have used the "pacing out" method on spinning disk's to conclude that more of them will fit per revolution than ought to be measured when the speed is close to zero. And that's supposed to be a special relativity problem.

But even if one walks there is acceleration, despite overall speed being uniform, because the feet are planted while the body's momentum does the rest.

You're comparing apples and oranges. In your scenario, the rulers are momentarily accelerated from a rest state with Betty to a rest state with the "starting" point and the ending flag. In the spinning disk there is constant acceleration.

Also, there is neither any assurance that the Proper Lengths under both conditions before and after acceleration are the same (but you can stipulate that) nor that any particular way that Betty ejects that rulers results in them butting up against each other (but you can stipulate that). If you make both stipulations, then you have just answered your question and the proplem becomes of no interest because you have just glossed over the real issues that Special Relativity can't handle.

 

[HALON]

You're comparing apples and oranges.

Speaking of which..

Length contraction under conditions of constant acceleration in a rotation, compared to between inertial states, seems more intuitive. A rotating body and an inertial body can compare data in real time if their separation is constant; everything is asymmetric. It’s useful too, as evidenced by GPS for our devices.

Compare how messy the physics is for a twin to travel to some faraway planet and back, and having to account for simultaneity, and positive and negative acceleration and all the weird experiences in between. Even when two inertial bodies pass each other what they see is not “real” because everything is suspended in symmetry, so to speak. They can’t interact. You have to wait for the symmetry to break to compare data.

 

[ghwellsjr]

You're comparing apples and oranges.

Speaking of which..

Length contraction under conditions of constant acceleration in a rotation, compared to between inertial states, seems more intuitive. A rotating body and an inertial body can compare data in real time if their separation is constant; everything is asymmetric.

It's not intuitive to me.

I think you are extrapolating the asymmetric Time Dilation between those two bodies and assuming that a similar trivial Length Contraction relationship also exists. The reason why it is trivial for Time Dilation is that we conceptualize clocks that have no dimensions and which maintain their ideal time keeping abilities under any acceleration. But you can't do the same thing with extended bodies specifically where you want to discuss Length Contraction. As I have said before, Special Relativity can't answer the question of how a body is deformed under acceleration and so you can't just set up a scenario by simply saying that you have two identical bodies, one inertial and the other rotating around it. You have to supply additional information on the changing shape of the rotating object.

If you want to make claims that it is intuitive, please actually set up a precise scenario with all the required details and then show how each body measures the Length Contraction of the other body.

It's useful too, as evidenced by GPS for our devices.

What evidence is there for Length Contraction by GPS in our devices? Are you thinking about Time Dilation?

Compare how messy the physics is for a twin to travel to some faraway planet and back, and having to account for simultaneity, and positive and negative acceleration and all the weird experiences in between.

Your rotating body scenario is messy because you are trying to explain Length Contraction with it. The twin scenario is very well understood and precisely defined under Special Relativity and nothing is weird about it because we always choose to ignore the Length Contraction of the traveling twin. I agree that if we wanted to include the Length Contraction of the traveling twin as a result of his accelerations, then Special Relativity would be inadequate but I have never seen an example of where anyone asked or anyone addressed that issue. Can you?

Even when two inertial bodies pass each other what they see is not "real" because everything is suspended in symmetry, so to speak. They can't interact. You have to wait for the symmetry to break to compare data.

No, what they actually see and measure is very real. Why would you say something like that? And they can interact. Why would you say they can't? They can certainly compare data under a symmetrical situation. Why do you think otherwise?

Maybe before you try to understand accelerating bodies, you should learn how Special Relativity deals with inertial bodies. It's really very simple. Einstein said so. And he should know.

 

[HALON]

It's not intuitive to me.

I think you are extrapolating the asymmetric Time Dilation between those two bodies and assuming that a similar trivial Length Contraction relationship also exists.

Actually, yes, that’s what I was thinking- time dilation, or $γ=1/\sqrt{1-v^2/c^2}$. I am aware of the difficulty in finding direct evidence for length contraction. Computer modelling of the length contraction of particles is just that, a model. (There may be other evidence that I’m not aware of, or can't understand). In any case I just imagine $γ$ acts as a kind of magnification factor when we apply $e=γmc^2$ to the rotating body. Because the total energy of the body’s system is invariant we need to multiply the previous energy mass conversion result by $1/γ$ to bring it back to terms. So it’s canceled out. Length contraction is just the cancelling out procedure for time dilation. I struggle with the idea physical bodies deform due to length contraction; I don’t get it. It’s like saying a body viewed through binoculars must deform to fit into our normal view.

What evidence is there for Length Contraction by GPS in our devices? Are you thinking about Time Dilation?

Yes, I was thinking of time dilation. Length contraction just balances the books.

Your rotating body scenario is messy because you are trying to explain Length Contraction with it.

I concede I was thinking of time, not length. To me, length contraction is not as real as time dilation because we can’t measure it directly. So what I really meant was that conceptually, time dilation in a rotation can be measured directly as it happens, continually. I guess the lengths of received wavelengths sent by the other body change, implying they contract in the rotating frame, but that’s not the kind of length that is meant.

No, what they actually see and measure is very real. Why would you say something like that? And they can interact. Why would you say they can't? They can certainly compare data under a symmetrical situation. Why do you think otherwise?

Sure, it’s a short interaction only. They can interact for an instant, and whoosh! They are separated. Bob can’t remark to Alice “you seem so slow today” and wait for Alice to say “so do you”. In that sense each other’s apparent slowing is not real. How can they compare data in real time? As Bob and Alice approach each other their signals are blue shifted, then there is an instant of interaction...followed by red shifted signal exchanges. But if Alice is rotating around Bob, Alice can tell Bob “you really are quick today” while Bob can confidently say “that’s because you are so slow compared to me” and carry on continual interactions. Alice's body length won’t change; she can lie next to a measuring rod parallel to the direction of rotation. We can only assume Alice's length contracts due to time dilation.

Maybe before you try to understand accelerating bodies, you should learn how Special Relativity deals with inertial bodies. It's really very simple. Einstein said so. And he should know.

You may be amused to know I have heard of Alfred Einstein and the Lorentz contraption. Something to do with pressing against the ether. Lorentz got a Nobel prize after he gave Alfred an equation, so Alfred stuck to the same terminology out of respect for the man who thought objects got squashed against the gas.

 

[ghwellsjr]

Actually, yes, that’s what I was thinking- time dilation, or $γ=1/\sqrt{1-v^2/c^2}$. I am aware of the difficulty in finding direct evidence for length contraction. Computer modelling of the length contraction of particles is just that, a model. (There may be other evidence that I’m not aware of, or can't understand).

What about the Michelson Morley Experiment where Length Contraction was devised as an explanation for the null result?

In any case I just imagine $γ$ acts as a kind of magnification factor when we apply $e=γmc^2$ to the rotating body. Because the total energy of the body’s system is invariant we need to multiply the previous energy mass conversion result by $1/γ$ to bring it back to terms. So it’s canceled out. Length contraction is just the cancelling out procedure for time dilation. I struggle with the idea physical bodies deform due to length contraction; I don’t get it. It’s like saying a body viewed through binoculars must deform to fit into our normal view.

Yes, I was thinking of time dilation. Length contraction just balances the books.

It's very easy to show that Length Contraction does not cancel out or balance out Time Dilation if you recall that Length Contraction applies only along the direction of motion whereas Time Dilation applies no matter the direction of motion. For example, consider a light clock where the light reflects back and forth perpendicular to the direction of motion and Length Contraction does not play a part in what is happening whereas if you rotate the light clock 90 degrees along the direction of motion it does.

I concede I was thinking of time, not length. To me, length contraction is not as real as time dilation because we can’t measure it directly. So what I really meant was that conceptually, time dilation in a rotation can be measured directly as it happens, continually. I guess the lengths of received wavelengths sent by the other body change, implying they contract in the rotating frame, but that’s not the kind of length that is meant.

Sure, it’s a short interaction only. They can interact for an instant, and whoosh! They are separated. Bob can’t remark to Alice “you seem so slow today” and wait for Alice to say “so do you”.

Of course Bob can remark to Alice and wait for a response back from Alice. Why are you saying this?

In that sense each other’s apparent slowing is not real.

Whatever is apparent to each of them is real. I don't understand why you say this.

How can they compare data in real time?

If they are separated, then they will have to wait and compare data later. Why is that a problem?

As Bob and Alice approach each other their signals are blue shifted, then there is an instant of interaction...followed by red shifted signal exchanges.

True. You have been talking about Doppler not Time Dilation. Do you know the difference?

But if Alice is rotating around Bob, Alice can tell Bob “you really are quick today” while Bob can confidently say “that’s because you are so slow compared to me” and carry on continual interactions.

But they cannot do it in real time. They have to wait for the signals to propagate between them just like in the non-rotation case. Why do you see a significant difference between the two cases? I don't understand why you think one case is more real than the other.

Alice's body length won’t change; she can lie next to a measuring rod parallel to the direction of rotation. We can only assume Alice's length contracts due to time dilation.

Alice's body length won't change from what? Do you realize that you can place a dozen measuring rods made of different materials side by side and them subject them to extreme identical acceleration and they may all end up different lengths? There's just no way to address this issue with Special Relativity.

You may be amused to know I have heard of Alfred Einstein and the Lorentz contraption. Something to do with pressing against the ether. Lorentz got a Nobel prize after he gave Alfred an equation, so Alfred stuck to the same terminology out of respect for the man who thought objects got squashed against the gas.

The difference between Lorentz's explanation is that he thought it was necessary to understand Length Contraction in terms of an absolute stationary ether through which we on the surface of the Earth are not stationary while Einstein realized that the same equations would work just as well if you assumed that we were stationary in that ether (in effect). That's why he called his theory simple.

 

[HALON]

What about the Michelson Morley Experiment where Length Contraction was devised as an explanation for the null result?

Length contraction was devised as an explanation, yes, but what experiment directly shows a “yardstick” to Lorentz contract? Only the number of ticks in a clock contract which, of course, is what is predicted by the length contraction hypothesis. So it is indirect evidence. I'm not saying it's not enough evidence to satisfy me. But it makes me wonder if length itself is a kind of abstraction.

It's very easy to show that Length Contraction does not cancel out or balance out Time Dilation if you recall that Length Contraction applies only along the direction of motion whereas Time Dilation applies no matter the direction of motion. For example, consider a light clock where the light reflects back and forth perpendicular to the direction of motion and Length Contraction does not play a part in what is happening whereas if you rotate the light clock 90 degrees along the direction of motion it does.

What I meant by “cancelling out” was in the sense of “normalization” so that proper time and proper lengths remain invariant in the moving frame. When you say time dilation applies no matter the direction of motion you can imagine a body’s proper time extending infinitely, like an expanding balloon without boundary. To impose a boundary we must first specify a value. Then we can make the balloon’s surface contract parallel (every which way) to the time expansion because it is stretched by whatever value of time volume we specified. But we still can’t measure this contraction directly. It’s existence is implied by using clocks, not yardsticks.

Of course Bob can remark to Alice and wait for a response back from Alice. Why are you saying this?

I was thinking of the case where Alice moves away from Bob. Communications are affected by feedback delay.

Whatever is apparent to each of them is real. I don't understand why you say this.

It's only a minor point. Alice might have died, but Bob may still be receiving transmissions and think she’s alive. The delay causes phantoms.

You have been talking about Doppler not Time Dilation. Do you know the difference?

This is my understanding. Between inertial frames, a clock moving toward Bob will seem to run fast right up until the point it reaches Bob. Then for an instant, the clock looks like it's running slow. Now, if the clock moves away it will seem to run even slower than the rate it runs according to time dilation. So the Doppler Effect is kind of independent of time dilation. However, the situation is simpler for a rotation. Here, what is called the Transverse Doppler Effect results in the perception agreeing with actual time rates, for both inertial and non-inertial observer, if the separation is constant. It's only when Alice leaves her orbit of Bob that the mismatch between signals and actual clock time appears.

Alice's body length won't change from what? Do you realize that you can place a dozen measuring rods made of different materials side by side and them subject them to extreme identical acceleration and they may all end up different lengths? There's just no way to address this issue with Special Relativity.

I know that. But any evident length contraction due to material deformation would not be due to the Lorentz contraction.

But they cannot do it in real time. They have to wait for the signals to propagate between them just like in the non-rotation case. Why do you see a significant difference between the two cases? I don't understand why you think one case is more real than the other.

Both cases are objectively real, it’s just that the currency of feedback between negligibly separated bodies in the rotation example makes it seem more relevant. In both cases there is a delay between propagation and reception. Yet in the rotation example the delay is minimal if Bob and Alice are close enough, which is as real as “real time” gets.

The difference between Lorentz's explanation is that he thought it was necessary to understand Length Contraction in terms of an absolute stationary ether through which we on the surface of the Earth are not stationary while Einstein realized that the same equations would work just as well if you assumed that we were stationary in that ether (in effect). That's why he called his theory simple.

It's a very simple theory. I wish I'd thought of it.

 

[ghwellsjr]

Length contraction was devised as an explanation, yes, but what experiment directly shows a “yardstick” to Lorentz contract? Only the number of ticks in a clock contract which, of course, is what is predicted by the length contraction hypothesis. So it is indirect evidence. I'm not saying it's not enough evidence to satisfy me. But it makes me wonder if length itself is a kind of abstraction.

Length has a precise definition that is consistent with all measurements and all evidence. But it is also dependent on the frame of reference which I guess is why you think of it as an abstraction.

What I meant by “cancelling out” was in the sense of “normalization” so that proper time and proper lengths remain invariant in the moving frame. When you say time dilation applies no matter the direction of motion you can imagine a body’s proper time extending infinitely, like an expanding balloon without boundary. To impose a boundary we must first specify a value. Then we can make the balloon’s surface contract parallel (every which way) to the time expansion because it is stretched by whatever value of time volume we specified. But we still can’t measure this contraction directly. It’s existence is implied by using clocks, not yardsticks.

Proper Time and Proper Length are defined in the rest frame of the object, not a frame in which it is moving. I can't make sense of the rest of your paragraph except for the last sentence. Nowadays, length is not just implied by using a clock, it is defined by using a clock.

You should quit thinking of Length Contraction as something that happens to a body as a result of its acceleration but rather simply as a result of applying the Lorentz Transformation to the coordinates of a body when you change from one Inertial Reference Frame to another IRF moving with respect to the first one. It's simply a coordinate effect. As such, it doesn't have to be measured. It's like defining two temperature scales and being concerned about finding some experiment to prove that the formula for converting from one scale to the other is experimentally verifiable.

I was thinking of the case where Alice moves away from Bob. Communications are affected by feedback delay.

It's only a minor point. Alice might have died, but Bob may still be receiving transmissions and think she’s alive. The delay causes phantoms.

The transmissions wouldn't deceive him. If she says she's still alive at a particular age, then he will think she is still alive at that age. If she dies at some age and the transmissions stop, then later when he notices the lack of transmissions he can deduce the age at which she died. I don't know why you are concerned about these issues.

Also, when you say "Alice might have died" you are implying that there is an absolute time for which such a statement would be true. Even in Bob's rest frame, where there is a precise definition of simultaneity, it is understood that Bob cannot determine the coordinates of distant events until the evidence of them propagate to him at the speed of light according to his rest frame.

This is my understanding. Between inertial frames, a clock moving toward Bob will seem to run fast right up until the point it reaches Bob. Then for an instant, the clock looks like it's running slow. Now, if the clock moves away it will seem to run even slower than the rate it runs according to time dilation. So the Doppler Effect is kind of independent of time dilation. However, the situation is simpler for a rotation. Here, what is called the Transverse Doppler Effect results in the perception agreeing with actual time rates, for both inertial and non-inertial observer, if the separation is constant. It's only when Alice leaves her orbit of Bob that the mismatch between signals and actual clock time appears.

Yes, in the rotational scenario, the Transverse Doppler equals the Time Dilation but only for the one particular IRF in which the non-rotating body is at rest. In other IRF's they are not equal. I fail to see why you are placing so much emphasis on one particular scenario. Special Relativity handles all scenarios where we can ignore the effects of gravity equally well.

I know that. But any evident length contraction due to material deformation would not be due to the Lorentz contraction.
Both cases are objectively real, it’s just that the currency of feedback between negligibly separated bodies in the rotation example makes it seem more relevant. In both cases there is a delay between propagation and reception. Yet in the rotation example the delay is minimal if Bob and Alice are close enough, which is as real as “real time” gets.

If you are trying to show a relativistic effect, then you can't relegate it to the realm of negligibility or the effect will go away. What you are talking about are examples such as where we ignore a finite acceleration interval when the total scenario is hundreds of times longer or where we ignore the finite size of a spaceship when the distance it is traveling is millions of times greater.

It's a very simple theory. I wish I'd thought of it.

 

[HALON]

Length has a precise definition that is consistent with all measurements and all evidence. But it is also dependent on the frame of reference which I guess is why you think of it as an abstraction.

OK

Proper Time and Proper Length are defined in the rest frame of the object, not a frame in which it is moving.

The rest frame is also a uniform moving frame if there is no acceleration.

I can't make sense of the rest of your paragraph except for the last sentence. Nowadays, length is not just implied by using a clock, it is defined by using a clock.

It's very easy to show that Length Contraction does not cancel out or balance out Time Dilation if you recall that Length Contraction applies only along the direction of motion whereas Time Dilation applies no matter the direction of motion.

Your observation about time not being dependent on direction (and the fact length is defined by time) leads to a geometric description. Namely, a body’s proper time extends in all directions, like a bubble. That's the part that didn't make sense to you, but I guess it's just a heuristic and nothing more. I blame all those introductory textbooks that inculcated me with the concept of relativistic mass, which is just mass multiplied by the time dilation factor; it's how the bubble idea arose in my mind.

You should quit thinking of Length Contraction as something that happens to a body as a result of its acceleration but rather simply as a result of applying the Lorentz Transformation to the coordinates of a body when you change from one Inertial Reference Frame to another IRF moving with respect to the first one. It's simply a coordinate effect. As such, it doesn't have to be measured. It's like defining two temperature scales and being concerned about finding some experiment to prove that the formula for converting from one scale to the other is experimentally verifiable.

OK

The transmissions wouldn't deceive him. If she says she's still alive at a particular age, then he will think she is still alive at that age. If she dies at some age and the transmissions stop, then later when he notices the lack of transmissions he can deduce the age at which she died. I don't know why you are concerned about these issues.

OK

Also, when you say "Alice might have died" you are implying that there is an absolute time for which such a statement would be true. Even in Bob's rest frame, where there is a precise definition of simultaneity, it is understood that Bob cannot determine the coordinates of distant events until the evidence of them propagate to him at the speed of light according to his rest frame.

OK

Yes, in the rotational scenario, the Transverse Doppler equals the Time Dilation but only for the one particular IRF in which the non-rotating body is at rest. In other IRF's they are not equal. I fail to see why you are placing so much emphasis on one particular scenario. Special Relativity handles all scenarios where we can ignore the effects of gravity equally well.

OK

If you are trying to show a relativistic effect, then you can't relegate it to the realm of negligibility or the effect will go away. What you are talking about are examples such as where we ignore a finite acceleration interval when the total scenario is hundreds of times longer or where we ignore the finite size of a spaceship when the distance it is traveling is millions of times greater.

OK

 

[ghwellsjr]

Proper Time and Proper Length are defined in the rest frame of the object, not a frame in which it is moving.

The rest frame is also a uniform moving frame if there is no acceleration.

The term "rest frame" has no meaning by itself. It's a shorthand way of saying a frame in which a particular object is at rest so you must always include the full expression, "the rest frame of the object".

You can always transform the coordinates of the rest frame of an object to the coordinates of another frame which is moving with respect to the rest frame but those are two different frames so that leaves your statement in limbo land. I don't know what you mean or why you would say that.

I can't make sense of the rest of your paragraph except for the last sentence. Nowadays, length is not just implied by using a clock, it is defined by using a clock.

It's very easy to show that Length Contraction does not cancel out or balance out Time Dilation if you recall that Length Contraction applies only along the direction of motion whereas Time Dilation applies no matter the direction of motion.

Your observation about time not being dependent on direction (and the fact length is defined by time) leads to a geometric description. Namely, a body’s proper time extends in all directions, like a bubble. That's the part that didn't make sense to you, but I guess it's just a heuristic and nothing more. I blame all those introductory textbooks that inculcated me with the concept of relativistic mass, which is just mass multiplied by the time dilation factor; it's how the bubble idea arose in my mind.

I think you have come to a wrong conclusion. Are you thinking that time stops for a photon, so that the time of each tick of a clock (so to speak) propagates outward in all directions at the speed of light like an expanding soap bubble? Is that what you're thinking?

 

[HALON]

The term "rest frame" has no meaning by itself. It's a shorthand way of saying a frame in which a particular object is at rest so you must always include the full expression, "the rest frame of the object".

You can always transform the coordinates of the rest frame of an object to the coordinates of another frame which is moving with respect to the rest frame but those are two different frames so that leaves your statement in limbo land. I don't know what you mean or why you would say that.

Yes I think I understand your point. I just meant the rest frame of the object with respect to the coordinates of another object.

My next answer is longer than I thought it would be.

I think you have come to a wrong conclusion. Are you thinking that time stops for a photon, so that the time of each tick of a clock (so to speak) propagates outward in all directions at the speed of light like an expanding soap bubble? Is that what you're thinking?

I'll put it in terms of the Doppler effect. When the distance between the signal emitter and the receiver widens, more wavelengths will fill the wider distance which causes the receiver to perceive them as a lower frequency as the signal is "stretched" over a longer distance. And the converse is true when the distance shortens. But in the very different circumstance of one body rotating about another body, the radial distance between them is constant. Now the central body receives a lower frequency, while the rotating body receives a higher frequency. This is called the transverse Doppler effect. So rather than the signal filling a longer or shorter distance, in this situation the signals fill a larger or smaller time volume. I don't know how else to picture it. (You can draw it quite simply using each clock "tick" as the radius of the time bubble, and the Lorentz transformation is the same). Anyway, Einstein said a body's acceleration is equivalent to a gravitational field- which is associated with mass. So if you use $e=γmc^2$ you can describe the bubble's increase in relativistic mass and come to an analogous conclusion regarding a body's relative increase in mass. Relative and relativistic mean different things. To illustrate the idea, see this image from Wikipedia

http://en.wikipedia.org/wiki/Gravitational_redshift#mediaviewer/File:Gravitational_red-shifting2.png

A body with greater relative mass receives a higher frequency of wavelengths, just as a body with greater relativistic mass does. You can re-imagine the larger sphere representing the rotating body compared to the central smaller sphere. But if you do so, the sphere's shown are now filled with relative time, not relative mass. (Or you can say each is composed of different relativistic mass, but not necessarily of different relative masses.).

Einstein introduced the equivalence principle. But equivalence does not mean identical. As I'm trying to convey, relativistic mass is not identical to relative mass. But as long as this distinction is clear, then it's OK to say a body's relativistic mass increases while its relative length contracts, although it's kind of using mixed terminology. Maybe that's why the term relativistic mass is avoided nowadays. In my early readings it was difficult to understand why writers would say the relativistic mass would increase, while elsewhere they would say it's length contracted. The distinction between relativistic and relative were not clear in the textbooks I read.

 

[Simon Bridge]

Yes I think I understand your point. I just meant the rest frame of the object with respect to the coordinates of another object.

I don't think that means anything - you can only have motion wrt a rest frame ... which is the frame in which some observer is at rest.

You can talk about how the rest frame of an object is moving wrt the rest frame of another object - in special relativity that would just involve stating the relative velocity of the two frames. But in that case, "frame" has the same meaning as "rest frame". You've seen this in introductory lessons which talk about the S frame and the S' frame. S' is the rest frame of observer O' and S is the rest frame for observer O. It is usually set up so that S' moves at speed v in the +x direction in frame S while S moves at (the same) speed v in the -x direction in the S' frame.

When the distance between the signal emitter and the receiver widens, more wavelengths will fill the wider distance which causes the receiver to perceive them as a lower frequency as the signal is "stretched" over a longer distance.

... um... when the receiver moves away from the emitter, the wave peaks arrive further apart in time - which results in the reduced frequency.

Or do you really mean that the farther apart receiver and emmitter, the longer the wavelength?
Even when they are stationary with respect to each other?

Note: gravity is subject to GR, your questions are in SR. Please try to avoid mixing the models up.
You also need to be more careful with your descriptions ... i.e.

in this situation the signals fill a larger or smaller time volume...

Time has only one dimension so it cannot have a volume. So what is it that you are calling a "time volume"?

The old "relativistic mass" is better understood as part of kinetic energy. "Rest mass" is just "mass" or "invarient mass". You are correct that it is easy to get confused when you use the term "relativistic mass" - so just don't use the term.

I'll leave ghwellsjr to decide if you have made the mistake suspected - it sounds like that to me.

 

[HALON]

I don't think that means anything - you can only have motion wrt a rest frame ... which is the frame in which some observer is at rest.

You can talk about how the rest frame of an object is moving wrt the rest frame of another object - in special relativity that would just involve stating the relative velocity of the two frames. But in that case, "frame" has the same meaning as "rest frame". You've seen this in introductory lessons which talk about the S frame and the S' frame. S' is the rest frame of observer O' and S is the rest frame for observer O. It is usually set up so that S' moves at speed v in the +x direction in frame S while S moves at (the same) speed v in the -x direction in the S' frame.

I understand that.

... um... when the receiver moves away from the emitter, the wave peaks arrive further apart in time - which results in the reduced frequency.

You could look it at that way too. When a train blows its whistle while moving away, the sound waves must cover the extra distance before reaching the observer. Doesn’t a moving light source follow the same principle? We have red-shifts to indicate stars are moving away.

Or do you really mean that the farther apart receiver and emmitter, the longer the wavelength?

Not quite. If emitter and receiver are not moving with wrt each other then the wavelength is what it is in the rest frame of the observer. You need to introduce acceleration in an orbit for asymmetry to arise.

Even when they are stationary with respect to each other?

This is the fascinating part. They are not exactly stationary; one body is rotating about the central observer. It was pointed out to me that the central observer will receive red-shifted signals from the rotating emitter, while the rotating emitter must therefore receive blue-shifted signals from the central emitter. Again, it was pointed out to me this is called the transverse Doppler effect. Yet the signals are not covering any extra or lesser distance, they are only covering dilated time and contracted time, if that makes sense.

Note: gravity is subject to GR, your questions are in SR. Please try to avoid mixing the models up.
You also need to be more careful with your descriptions ... i.e. Time has only one dimension so it cannot have a volume. So what is it that you are calling a "time volume"?

Time is a scalar; distance is a vector. So yes, it is alien to speak of time as having volume. But in a strictly confined context you can use it to describe a calculation. I’ll try be careful...and I will claim in advance there is nothing new about it, or contradictory. Here goes:

It strikes me that in the rotation case we have GR and SR rolled into one. There is constant acceleration of the angular velocity- that’s the GR part- and there's time dilation and length contraction- which is the SR part. After a few steps in calculation, we find the diagonal path (DP) traced by a photon in a moving light clock relative to a "stationary frame" may be given as $1h/(c^2-v^2)^{1/2}$, where $h$ is the separation between the mirrors. It turns out the result is always longer than $1$ for the light clock that is moving (when viewed from a stationary frame). Now, imagine the DP of a photon in a light clock that is momentarily co-moving with the rotating frame for some very short distance at uniform speed (i.e. as part of a polygon fitted around the circle). Then the wider DP for the co-mover compared to the vertical path traced by a photon in a relatively “stationary” light clock (which always equals $1h/c$) must correspond to a higher frequency of received wavelengths if sent from the central frame. So the wider DP exactly equals the time dilation factor, $1/(1-v^2/c^2)^{1/2}$, if you substitute $1$ for $h$ in the first equation. This surely isn’t new.

When I think of dilation I think of something that "dilates" like the pupil in the eye. The higher received wavelengths (the Transverse Doppler effect) “fit” into the dilated dimension of the rotating frame. Because the dimension is dilated, more wavelengths have to be accommodated for each “tick” of the clock that approaches synchronization with the earlier mentioned co-moving light-clock. Therefore the wavelengths travel longer in the dimension of time (from the "stationary" view) just like they travel longer in the dimension of distance between widening inertial frames. We can view it as a relativistic time expansion so the properties of mass expand relativistically too, which in no way should be confused with absolute quantities of mass.

The old "relativistic mass" is better understood as part of kinetic energy. "Rest mass" is just "mass" or "invarient mass". You are correct that it is easy to get confused when you use the term "relativistic mass" - so just don't use the term.

There are interesting papers pro and against the use of “relativistic mass”. Some properties depend on motion relative to the observer (TR Sandin, In Defense of Relativistic Mass, American Journal of Physics, 1991) I found Sandin’s argument persuasive. Rest mass is rest mass, which does not change just because its relativistic mass changes. Anyway, that sounds like another thread starter. But I think it comes down to being careful with the term and its correct context, rather than total avoidance.

 

[Simon Bridge]

You could look it at that way too. When a train blows its whistle while moving away, the sound waves must cover the extra distance before reaching the observer. Doesn’t a moving light source follow the same principle? We have red-shifts to indicate stars are moving away.

How do you know if it is the light source or the light observer who is moving?
You keep making this mistake in your descriptions. Please be precise about what you mean.

Not quite. If emitter and receiver are not moving with wrt each other then the wavelength is what it is in the rest frame of the observer. You need to introduce acceleration in an orbit for asymmetry to arise.

Oh you intended your statements to be read in the context of a non-inertial reference frame. I'll leave that to others to avoid hitting you with too many voices at once.

Time is a scalar; distance is a vector.

Distance is a scalar also - it is the magnitude of the displacement vector. I'm being pedantic because I suspect that your habit of being imprecise is the cause of much confusion between yourself and those trying to talk to you.

You'll also notice that, in relativity, time is another length.
It is common to use the invariant interval to define a metric as a way to deal with geometry in space-time.

So yes, it is alien to speak of time as having volume. But in a strictly confined context you can use it to describe a calculation. I’ll try be careful...and I will claim in advance there is nothing new about it, or contradictory.

Fair enough - I'll let someone else wade through that ;)
Still don't see what you mean by the volume of time.

When I think of dilation I think of something that "dilates" like the pupil in the eye.

No wonder you are having trouble - time is 1D and the pupil of an eye is 2D, so there is no useful simile to be had there either.

Try to avoid poetic language in your descriptions if you want to be understood.
Perhaps you can demonstrate how the wave fits into the dilated time by a space-time diagram or by reference to the metric or something more standard like that?

I think it comes down to being careful with the term [relativistic mass] and its correct context, rather than total avoidance.

Avoid it all together. You are having enough problems with imprecise and ambiguous terms already.

Meantime I'll watch how others answer you some more ;)

 

[HALON]

No wonder you are having trouble - time is 1D and the pupil of an eye is 2D, so there is no useful simile to be had there either.

Try to avoid poetic language in your descriptions if you want to be understood.
Perhaps you can demonstrate how the wave fits into the dilated time by a space-time diagram or by reference to the metric or something more standard like that?

I don’t have the skills to arrive at the equivalence principle using space-time diagrams. Maybe somebody can explain that. This is how I get there:

Time is 1D, but a clock face is 2D (and potentially even 3D). From the outset, this is a purely idealized imaginary clock (old fashioned circular type) but what it’s made of is irrelevant.

The double diagonal path of a photon in the Michelson-Morley experiment is $2h/(c^2-v^2)^{1/2}$. For simplicity, let the separation between the mirrors $h$ and speed of light $c$ be equal to $1$. Next, plug in any value for $v$ which is a proportion of $c$ and calculate. Whatever you found can equal the big hand’s length, the radius $r$ of the imaginary clock. So the double diagonal path = $r$

Here is an exercise. You found the radius already. Now find the circumference and area of the clock face when $v=0$. Now divide the circumference by the area. What does it equal? Next divide the area by the circumference. What does it equal? (Hint: circumference=$2πr$ and area=$πr^2$)

Now do the same exercise for any value of $v$, like 0.6, 0.8 or whatever. Do you notice anything familiar? Compare the results with the Lorentz factor and length contraction factor!

The imaginary clock face’s relativistic mass has increased by $γ$. Because energy is conserved in a system, the big hand’s absolute perimeter speed is the same as what it was when $v=0$. So naturally it will take longer to complete a revolution of the dial, because some of the energy has been diverted into the dimension of time. It will take $γ$ times longer to complete a revolution.

This is what is meant by time dilation and I credit Brian Greene, author the Elegant Universe for helping me think this way.

When $v$ increases, the double diagonal path increases in length. Imagine a stream of photons bouncing between the mirrors. As the path traced by the stream lengthens, then whoever travels with the mirrors (i.e as co-moving temporary observers) will see the same frequency of light for each cycle of reflection. But a perceived light sent from an inertial central frame will increase in frequency by $γ$. That’s because some of the wavelengths have been diverted into the dimension of time. More of them are crammed into this dimension, due to the asymmetry of time between accelerating and inertial bodies. So they are perceived as being more frequent.

Now, this imaginary clock’s hand rotates about the centre. Thus the hand is constantly accelerating. As the clock-face’s relativistic mass increases, the frequency of centrally emitted light as perceived in the clock-face’s frame increases by an equivalent amount to the case of acceleration caused by gravity. That’s called the equivalence principle.

And that’s how, in my bumbling way, I see GR and SR morphing into one.

Avoid it all together. You are having enough problems with imprecise and ambiguous terms already.

Avoid relativistic mass? I didn’t invent the term. Relativistic mass helps me conceive the equivalence principle directly and simply. I agree it is used imprecisely and ambiguously by others. Some authors employ relativistic mass to explain why an object can’t go faster than light. They say it takes more and more energy to accelerate a larger and larger relativistic mass, implying that relativistic mass is something that gets more physically massive. That’s just wrong.

 

[PeterDonis]

I credit Brian Greene, author the Elegant Universe for helping me think this way.

This, IMO, is a good illustration of why a number of people here on PF (including me) cringe whenever Brian Greene is referred to. I've lost count of the number of threads in which we've had to correct misconceptions caused by his books and TV specials. The problem is not that what he says is wrong, exactly; it's that the concepts he gives you do not generalize: you can only apply them in the narrow scenarios he uses for illustration. Try to reason from them to further concepts, or in other situations, and you will only end up more confused.

I'm not sure why Greene (and others--Michio Kaku comes to mind) insists on describing relativity (and quantum mechanics) in such a way, but I suspect it's because he doesn't actually expect you to reason from what he says. He expects you to just say "oh, wow!" and move on. So when people actually try to reason from what he says to apply it to other situations--i.e., they treat what he says as actually part of a generative theory, instead of just "oh, wow!" illustrations--it doesn't work, because he didn't give you a set of concepts that you can correctly reason from in other situations.

 

[Simon Bridge]

This, IMO, is a good illustration of why a number of people here on PF (including me) cringe whenever Brian Greene is referred to.

Me too.

I'm not sure why Greene (and others--Michio Kaku comes to mind) insists on describing relativity (and quantum mechanics) in such a way, but I suspect it's because he doesn't actually expect you to reason from what he says. He expects you to just say "oh, wow!" and move on.

Thats pretty much it. The aim is to convey the wonder and majesty of the science they are talking about without bothering the audience with anything deemed "too technical" while entertaining them with pretty visuals. The shows and books are entertainment only, and that is the sort of thing that sells.

The best advise at this point it to go read a real science book.

 

[zbe]

This reminds me of a clip of Brian Greene on The Big Bang Theory. :tongue:

 

[HALON]

Should I read this book? Namely, It's About Time: Understanding Einstein's Relativity by N. David Merman who states on page 63

--The slowing down of moving clocks is often referred to by the deplorable term "time dilation".[You tell 'em Dave!] It is deplorable because it suggests in some vague way that "time itself" (whatever that might be) is expanding when a moving clock runs slowly.--

On the back cover of the book :

--N.David Mermin is a member of the National Academy of Sciences and won the first Julius Edgar Lilienfeld Prize of the American Physical Society. His books include Solid State Physics, Boojums All the Way Through, and Space and Time in Special Relativity--

The back cover even has a positive review from -Brian Greene, Columbia University

 

[PhysicistMike]

Should I read this book? Namely, It's About Time: Understanding Einstein's Relativity by N. David Merman who states on page 63

--The slowing down of moving clocks is often referred to by the deplorable term "time dilation".[You tell 'em Dave!] It is deplorable because it suggests in some vague way that "time itself" (whatever that might be) is expanding when a moving clock runs slowly.--

The exact opposite of what he says is true since I think that clocks measure time and thus what clocks are doing is exactly what time is doing so it's correct to say that time itself is slowing down.

If you were to follow how the Lorentz transformation is derived then you'd see that the expression for the slowing of clocks is used to derive that transformation and that transformation tells us how time runs on other frames and we use that to show that the laws of physics behave the same in all frames of reference.

 

[Doc Al]

Should I read this book? Namely, It's About Time: Understanding Einstein's Relativity by N. David Merman who states on page 63

Despite that mysterious-sounding quote, the book is good and I recommend it. (Quote the entire paragraph and it will appear a bit less mysterious.) Laymen who want a good taste of relativity and who aren't afraid of a little algebra will get a lot out of it.

 

[losk]

Given that Michelson-Morley experiment lies at the heart of all this, does anyone know if it was every done while apparatus was in motion relative to Earth? As opposed to sitting in the lab.

 

[Simon Bridge]

Despite that mysterious-sounding quote, the book is good and I recommend it. (Quote the entire paragraph and it will appear a bit less mysterious.) Laymen who want a good taste of relativity and who aren't afraid of a little algebra will get a lot out of it.

Always remembering that anyone can be quoted out of context, even highly qualified people can write rubbish, and there is no cause so worthy there are no idiots supporting it

Given that Michelson-Morley experiment lies at the heart of all this, does anyone know if it was every done while apparatus was in motion relative to Earth? As opposed to sitting in the lab.

That would be hard to do - the apparatus is easily messed up by vibrations. What would you expect to be different?

Note: The MME is not "at the heart of this" in the sense that if the experiment were overturned somehow then relativity would be wrong. SR and GR are accepted on a preponderance of evidence from many clever and concerted disproof-attempts over many years. It was a key experiment, but not the only one.

 

[losk]

Always remembering that anyone can be quoted out of context, even highly qualified people can write rubbish, and there is no cause so worthy there are no idiots supporting it

That would be hard to do - the apparatus is easily messed up by vibrations. What would you expect to be different?

Note: The MME is not "at the heart of this" in the sense that if the experiment were overturned somehow then relativity would be wrong. SR and GR are accepted on a preponderance of evidence from many clever and concerted disproof-attempts over many years. It was a key experiment, but not the only one.

MM was designed to prove the stationary aether, and it succeeded in disproving it. However, it says nothing about the light medium that moves just like bodies do, attracted to them by gravity, just like satellites are. Performing MM in a motion relative to Earth surface would clear that up. Or could bring up something entirely unknown. And in general, performing experiments that we're sure have nothing to prove can be illuminating, as history suggests. Most theory-overturning events happened when people thought they were doing one thing, but they actually did another. MM being a perfect example of that. I guess I am just surprised that people conducted many stationary MM experiments, but none in motion. It seems like they were hitting the same nail on the head, instead of trying another one... That's all, just odd. It can be done. Satellites in orbit move at 3+ km/s relative to Earth without vibrations, so it should be no problem to do...

If MM were overturned, that would not mean SR and GR are dead, but it would certainly mean that they are not entirely correct, and that we have to look for a better theory. Much like Newton's physics isn't dead by means of SR and GR, but isn't entirely correct either.

 

[Simon Bridge]

The GPS system is like a continuous, world-wide Michelson-Morley experiment, much more precise than the original experiment, and uses satellites at different altitudes as well as ground stations also at different altitudes. If MM is wrong, then GPS navigation is also wrong.

It we got different results from some satellite measurement we'd look for some influence in orbit that is throwing the experiment off rather than look to modify SR and GR itself. That's how good the theory is. It's like if you dropped your pen and saw that it went sideways instead of down ... would you need to modify Newtonian gravity, or would you look for some additional effect knocking the pen to the side?

Anyway - this is off topic.
You are being copeously answered in another thread.
https://www.physicsforums.com/showthread.php?t=765235