Is it time to "retire" time dilation and length contraction?

[PAllen]

Yes, I think that is the better approach.

Differential aging is a relatively standard term. Not sure where/when I first saw it, but it's a term I've used as distinct from time dilation for many years. One is invariant and one is frame dependent. Note that frame dependence doesn't necessarily mean unobservable, because you can materialize a frame implementing standard clock sync and observe standard clock synch between separated clocks. Any observer, analyzing your set up, would correctly predict your observation.

Note also that muons reaching the ground is an observation, and is not differential aging. Being a non-local series of observations (you have to find out that muons are created high in the atmosphere), it has multiple frame dependent explanations - time dilation or length contraction.

Based on this, I'm not so sure these concepts should be so deprecated just because they are frame dependent. Yes, you can just do an interval computation in any coordinates, but it seems useful to me to have terms to describe this scenario.

 

[Dale]

Several off topic posts have been removed

 

[Herman Trivilino]

That is invariant so it is differential aging.

So, is this an example of the dilated time $\gamma \Delta \tau$ being invariant? Or is it an example of $\gamma \Delta \tau$ not being a dilated time?

Or is there a third option I'm not seeing?

The thing that makes $\gamma \Delta \tau$ invariant in this case is that it's a proper time (time between two events that are not spatially separated) for the stay-at-home twin. So this makes it a special case. The thing I want to know is when I teach the twin paradox to non-majors am I cheating when I call this time dilation?

 

[PeterDonis]

The thing I want to know is when I teach the twin paradox to non-majors am I cheating when I call this time dilation?

I don't know that it's "cheating", but it might be confusing, since, as I said in a previous post, the term "time dilation" has two possible meanings. One is the invariant thing you describe. The other is something that is not invariant; it's frame-dependent (the fact that a moving clock "appears to run slow", which depends on your choice of frame). Using the same term for two things, one of which is invariant and one of which isn't, is going to cause confusion. As far as I know, nobody has tried any term except "time dilation" for the frame-dependent thing, so that seems like the best one to keep the term; but then we need to find a different term for the invariant.

 

[m4r35n357]

I don't know that it's "cheating", but it might be confusing, since, as I said in a previous post, the term "time dilation" has two possible meanings. One is the invariant thing you describe. The other is something that is not invariant; it's frame-dependent (the fact that a moving clock "appears to run slow", which depends on your choice of frame). Using the same term for two things, one of which is invariant and one of which isn't, is going to cause confusion. As far as I know, nobody has tried any term except "time dilation" for the frame-dependent thing, so that seems like the best one to keep the term; but then we need to find a different term for the invariant.

BTW thanks to everyone who has commented on this thread, I've enjoyed it more than I thought I would (I suppose I expected to be slagged off or ignored)!

I'm probably going to show my ignorance here, but that will only serve my point that the concepts are confusing ;) I most commonly hear/read about TD & LC in the context of just multiplying/dividing the two "observer" frame quantities by gamma. Now, if I have understood the Lorentz transform correctly, the "moving frame" length needs to be measured at different times, and the "moving frame" time at different positions. This is perhaps the root of my feeling that they are both unobservable, and rather contrived.

Now, since gamma is encoded in a rather obvious way in the spacetime interval, I am not surprised that people use the "divided" quantities as if they are nothing unusual, but I do find with that usage clumsy and "untidy".

Also, the idea that the rest-frame distance obligingly compresses itself at the whim of a traveler seems misleading too. I maintain that the (coordinate) distance traveled is just that (I suppose you can say that it "stretches back" when you get there, but, well, bah!). The time dilation is not so obviously misleading, but really what is wrong with "proper time" ? Aging is another word for that, but even that sounds a bit anthropomorphic to me.

So, now I have laid bare my (mis)understanding of the two concepts, perhaps you can understand why I find them confusing, and avoid them with a vengeance! When using the spacetime interval I can at least pretend to know what I am talking about ;)

I shall now brace myself . . .

 

[Alan McIntire]

In reply to slow thinker, the OBSERVED doppler effect is sqrt {(1-v/c/1 + v/c)} for objects moving apart,
sqrt {(1 + v/c)/(1-v/c)} for objects moving together. Plug in 4/5 c for v and you'll get 1/3 and three respectively

 

[PAllen]

In reply to slow thinker, the OBSERVED doppler effect is sqrt {(1-v/c/1 + v/c)} for objects moving apart,
sqrt {(1 + v/c)/(1-v/c)} for objects moving together. Plug in 4/5 c for v and you'll get 1/3 and three respectively

see post #84.

 

[SlowThinker]

I most commonly hear/read about TD & LC in the context of just multiplying/dividing the two "observer" frame quantities by gamma. Now, if I have understood the Lorentz transform correctly, the "moving frame" length needs to be measured at different times, and the "moving frame" time at different positions. This is perhaps the root of my feeling that they are both unobservable, and rather contrived.

Well I've been reading and thinking about TD&LC for so long that it feels natural that as my spaceship accelerates towards Alpha Centauri, the distance gets shorter and I age less during travel.
The main trouble I see is that the Relativity of Simultaneity is the most important effect, that
- can be explained without the need to understand TD&LC
- RoS is necessary for TD&LC to make sense
There are 2 sides to RoS:
When talking about a length-contracted spaceship, you always have to remember that the clock in the front show different time from the ones at the back (I'm always having trouble remembering which is which, probably later/older at the front).
Also, as the spaceship travels, it arrives at places where time is running slow, but there *already is* the future. So you still arrive at the destination 4 years later even if you spent just 1 year flying.

Hope this helps... or just ignore me

 

[SlowThinker]

In reply to slow thinker, the OBSERVED doppler effect is $\sqrt {(1-v/c)/(1 + v/c)}$ for objects moving apart, $\sqrt {(1 + v/c)/(1-v/c)}$ for objects moving together. Plug in 4/5 c for v and you'll get 1/3 and three respectively

Yes but that's introducing yet another effect, more derivations, and more formulas to remember.

 

[robphy]

In reply to slow thinker, the OBSERVED doppler effect is sqrt {(1-v/c/1 + v/c)} for objects moving apart,
sqrt {(1 + v/c)/(1-v/c)} for objects moving together. Plug in 4/5 c for v and you'll get 1/3 and three respectively

Yes but that's introducing yet another effect, more derivations, and more formulas to remember.

In Bondi's method, the doppler effect is more primitive (the Doppler Factor is an eigenvalue of the Lorentz Transformation)...
other effects (like time-dilation, length-contraction, velocity-composition, and the Lorentz transformation) are then derived from it.

 

[m4r35n357]

Yes but that's introducing yet another effect, more derivations, and more formulas to remember.

Hold on a second, I would definitely advocate learning about the Doppler effect. It is VERY real and essential to almost all astronomical and cosmological studies (and makes analyzing the twin paradox a doddle). Also the aberration of light (see steps 3 & 4 of my OP!). This is exactly the sort of interesting stuff that you can get into once you get over the trivia ;)

 

[SlowThinker]

Hold on a second, I would definitely advocate learning about the Doppler effect. It is VERY real and essential to almost all astronomical and cosmological studies (and makes analyzing the twin paradox a doddle). Also the aberration of light (see steps 3 & 4 of my OP!). This is exactly the sort of interesting stuff that you can get into once you get over the trivia ;)

Oh, I thought that the Doppler effect is used *in addition* to Lorentz transformation, not *instead of* it. It makes sense then, although I'm not really used to thinking in terms of Doppler effect.

Are you saying that it's worth it learning about aberration (I agree), or that the Doppler effect explains it? (How??)

 

[m4r35n357]

Oh, I thought that the Doppler effect is used *in addition* to Lorentz transformation, not *instead of* it. It makes sense then, although I'm not really used to thinking in terms of Doppler effect.

Are you saying that it's worth it learning about aberration (I agree), or that the Doppler effect explains it? (How??)

The Doppler effect and aberration both have the LT "built in". The Doppler effect shows how colours of objects change with relative motion, whilst aberration deals with changes in the position/shape of objects. Both these effects are visual, so you need 2 space dimensions and one time to describe them.

Please take a look that these videos I made, and read the explanation. There is a lot to take in, so don't expect to understand what is going on straight away, but treat it as a pointer to where SR can take you if you follow my advice (sorry if this sounds pretentious, it's not my intention).

BTW just to clarify, I might have given the impression that I oppose over-stressing the importance of TD/LC out of laziness. This is most definitely not the case, I do it in the interests of efficiency.

 

[SlowThinker]

whilst aberration deals with changes in the position/shape of objects. Both these effects are visual, so you need 2 space dimensions and one time to describe them.

So you replace the length contraction with aberration?

Please take a look that these videos I made, and read the explanation. There is a lot to take in, so don't expect to understand what is going on straight away, but treat it as a pointer to where SR can take you if you follow my advice (sorry if this sounds pretentious, it's not my intention).

I've seen the videos a few days ago but I can only access the first line of the explanation, so I can't quite understand what's going on.

 

[m4r35n357]

So you replace the length contraction with aberration?

I've seen the videos a few days ago but I can only access the first line of the explanation, so I can't quite understand what's going on.

See the bit where it says "more"? It's bedtime in the UK so I'll let you get on with it for now . . .

 

[SlowThinker]

See the bit where it says "more"? It's bedtime in the UK so I'll let you get on with it for now . . .

Nope, no such button. It seems Apple and Google don't quite cooperate.

Edit: Same on Android.

 

[Herman Trivilino]

Now, if I have understood the Lorentz transform correctly, the "moving frame" length needs to be measured at different times,

If it were measured at the same time it would be proper length.

and the "moving frame" time at different positions.

If it were measured at the same position it would be proper time.

These conclusions follow immediately from invariance of the interval.

This is perhaps the root of my feeling that they are both unobservable, and rather contrived.

They're definitely observable. And although they may seem contrived they are very real. There are plenty of people with you, though, in thinking that they are not pedagogically advisable. This thread has illuminated alternative ways of presenting SR without them, and has definitely spawned a lot of informative discussion.

 

[Herman Trivilino]

I don't know that it's "cheating", but it might be confusing, since, as I said in a previous post, the term "time dilation" has two possible meanings. One is the invariant thing you describe. The other is something that is not invariant; it's frame-dependent (the fact that a moving clock "appears to run slow", which depends on your choice of frame).

It seems to me, then, that differential aging is just a difference between two proper times, something that will therefore always be invariant.

In SR the definition of dilated time is $\gamma \Delta \tau$ where $\Delta \tau$ is a proper time and $\gamma=(1-\beta^2)^{-\frac{1}{2}}$ where $\beta$ is the relative speed of the observer. That's a frame-dependent quantity, except in the example I gave above which is perhaps not a strictly valid example of time dilation because it involves a change in $\beta$. If not a "cheat" then maybe a slight of hand?

Therefore would it be better to say that during the first half of the traveling twin's journey a proper time $\Delta \tau$ elapses on his ship and the stay-at-home twin measures this to be the dilated time $\gamma \Delta \tau$? Likewise for the return trip.

 

[PeterDonis]

It seems to me, then, that differential aging is just a difference between two proper times, something that will therefore always be invariant.

Yes.

would it be better to say that during the first half of the traveling twin's journey a proper time $\Delta \tau$ elapses on his ship and the stay-at-home twin measures this to be the dilated time ##\gamma \Delta \tau##? Likewise for the return trip.

"Measures" is perhaps not the best word here, because this is not a direct measurement the stay-at-home twin makes. He can calculate, after the fact, that, relative to his inertial frame, the traveling twin turned around when his clock read $\gamma \Delta \tau$. But he can't observe that directly. The only direct measurements he can make are observations of light signals coming from the traveling twin, showing images of the traveling twin's clock; he can see what the traveling twin's clock reads in those images, and measure the Doppler shift of the signals. That's it. Everything else is calculated, and using the word "measurement" for something that's calculated seems like a bad idea to me.

 

[Herman Trivilino]

Everything else is calculated, and using the word "measurement" for something that's calculated seems like a bad idea to me.

Well, usually the word "observe" is used.

Say the traveling twin agrees to send a signal back home when he arrives. The stay-at-home twin gets the signal, subtracts off the travel time of the signal, and arrives at a result. That is the result of a calculation. But isn't it the case that most measurements are the result of calculations?

 

[PeterDonis]

usually the word "observe" is used.

Yes, and it has the same problems. Unfortunately, there isn't really a good word to describe this; I often try to say "calculate", but that's cumbersome. Sometimes I've tried "judge", but that doesn't seem to help much.

Say the traveling twin agrees to send a signal back home when he arrives. The stay-at-home twin gets the signal, subtracts off the travel time of the signal, and arrives at a result. That is the result of a calculation.

Yes, that's the sort of calculation I had in mind.

But isn't it the case that most measurements are the result of calculations?

Not in the same way. For example, suppose the stay-at-home twin measures the Doppler shift of the signal from the traveling twin. That measurement is the "result of a calculation", in the sense that he can't directly detect the shift; he can only detect the frequency. He calculates the shift as the difference between the frequency he detects and the (presumed known) frequency of emission.

Now contrast this with the stay-at-home twin's calculation of the time of emission of the signal the traveling twin sends when he turns around. He directly measures the time of arrival of the signal. He subtracts off the travel time--but how does he know the travel time? He can't measure it directly, and it's not a previously known constant like the emission frequency of the light signal. He has to calculate it. How does he calculate it? Well, he knows the traveling twin's speed--or at least he knows what speed the traveling twin said he was going to use, and how long the traveling twin intended to travel, by his own clock, before he turned around. Or, he can watch the traveling twin continuously, detecting light signals from him all during his outward trip (assuming the traveling twin is emitting such signals), and use the Doppler measurements from those signals to verify the traveling twin's speed away from him. When he then receives the turnaround signal (which he will detect by the sudden shift in Doppler from redshift to blueshift), he can then go back and put together all those measurements and calculate the travel time of the turnaround signal based on the distance the traveling twin was when he emitted it. But all that is a lot more complicated, and involves more variables, than the simple calculation of the difference between received frequency and known emitted frequency.

To an extent this is a judgment call, of course; but I think it's clear that there's a big difference between the "calculation" of the Doppler shift and the calculation of the traveling twin's turnaround time, big enough to justify using the term "measurement" for the first but not the second.

 

[m4r35n357]

Nope, no such button. It seems Apple and Google don't quite cooperate.
View attachment 91990
View attachment 91991
Edit: Same on Android.

OK, Here's the text (I intend to revisit this in the near future to tighten it up a bit):

The twin "paradox" (in quotes because it is NOT a real paradox!) is a valuable learning tool for Special Relativity: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html

This is a series of visualizations of the journey from the point of view of the traveling twin, who flies 20 light years away from his home station then returns. The journey consists of four parts, joined together. The first quarter is an acceleration away from the station. During the second and third quarters the ship accelerates towards the station (so that at the half way point the ship is stationary 20 light years away). In the fourth quarter the ship accelerates away from the station in order to come to rest there.

The total coordinate travel time (shown as a red dot in the top left HUD clock) is 43.711/58.918 years for acceleration at earth/moon gravity levels, whilst proper time (green dot) is 12.101/38.694 years. The yellow dot represents the time the traveller would see on the station clock face through a very powerful telescope! The octahedral stations (spaced one light year apart and one light year to the left of the flight path) are all synchronized to coordinate time and rotate once over the course of the whole journey. There is a 2x2 light year wall one light year beyond the far end of the journey, and large rectangular frames every 5 light years. Where a floor is shown it is 1 light year per stripe, and there are small 1 ly milestone spheres along the way, with a larger one every five light years.

The flights are rendered without relativistic effects and then for two values of acceleration (currently Earth gravity and moon gravity). The distortion artifacts are due to aberration of light, the Doppler effect and the headlight effect. The Earth gravity videos exhibit some nice penrose-terrel "rotation" effects. Magenta markers in a circle show where you really are in the scene (Doppler shift = gamma for this circle), and grey markers show the circle where the doppler shift is 1 (gamma is in theory directly observable on this circle).

These videos were made with POV-Ray (http://www.povray.org/) and avconv/ffmpeg (https://www.ffmpeg.org/) video encoding software.

 

[Herman Trivilino]

Yes, and it has the same problems. Unfortunately, there isn't really a good word to describe this; I often try to say "calculate", but that's cumbersome. Sometimes I've tried "judge", but that doesn't seem to help much.

Perhaps "determine"?

The issue is that we're talking about an amount of time that passes between two events that are separated in the observer's space. (Otherwise, of course, we'd be talking about proper time.) So in that sense it's a quantity that can't be measured "directly" by that observer only because he can't be in two places at the same time. But it's still a very observable, measurable, determinable, and real amount of time. What we're looking for here is a word that's least likely to induce misconceptions. Perhaps there is no such optimal word and the best thing is to have ready a vocabulary of alternatives to be used interchangeably, exposing the listener to the variety.

Now contrast this with the stay-at-home twin's calculation of the time of emission of the signal the traveling twin sends when he turns around. He directly measures the time of arrival of the signal. He subtracts off the travel time--but how does he know the travel time? He can't measure it directly, and it's not a previously known constant like the emission frequency of the light signal. He has to calculate it. How does he calculate it? Well, he knows the traveling twin's speed--or at least he knows what speed the traveling twin said he was going to use, and how long the traveling twin intended to travel, by his own clock, before he turned around.

That's if the distance had not already been measured by some other means beforehand. If, for example, the trip is to the moon, he already knows the distance and can calculate the delay time of a light signal in advance. Then, the only thing needed is one subtraction.

He could even get around that by setting a clock to that much time before zero. When the signal is received it automatically stops the clock and the time can be read directly.

 

[m4r35n357]

BTW sources for the ray-traced videos are available on GitHub

 

[valentin mano]

We have two synchronized clocks and one of them is acceleratated near the speed of light.The GR approach is neaded here,because SR is symmetric by the Lorenz Transforms.

 

[Dale]

We have two synchronized clocks and one of them is acceleratated near the speed of light.The GR approach is neaded here,because SR is symmetric by the Lorenz Transforms.

Back in Einstein's day and the early years of GR, that was a common way to look at it. In modern terms GR is usually only considered to be involved when spacetime is significantly curved (I.E. when tidal gravity is important). Simply using tensors and non inertial coordinates in flat spacetime is not considered GR except insofar as flat spacetime is a trivial solution of the Einstein field equations.

 

[valentin mano]

I was just trying to say,that the twin paradox has nothig to do with the Special Relativity.The principle of equivalence(no tidal forces)is implied here.

 

[PeterDonis]

I was just trying to say,that the twin paradox has nothig to do with the Special Relativity.

And that is incorrect. The standard twin paradox is set in flat spacetime, and SR is entirely sufficient to analyze it.

The principle of equivalence(no tidal forces)is implied here.

First, the principle of equivalence does not say "no tidal forces", period. It says "no tidal forces are detectable in a small enough region of spacetime".

Second, "no tidal forces" means "flat spacetime", which again means SR is entirely sufficient.

Third, why is the lack of tidal forces important in analyzing the twin paradox?

 

[Chestermiller]

I really like what you said in your original post. As a relative newcomer to relativity, I also struggled with the many texts that I tried to learn from, because the material was presented so badly (even though I was an experienced professional in engineering). Eventually, I was able to put the pieces of the puzzle together on my own, but not without considerable effort. So I totally agree that there has to be a better way of teaching this subject matter than the way it has traditionally been done.

I like the curriculum you laid out in your original post. In my judgement, the entry point to understanding relativity in depth starts with the Lorentz Transformation. So getting to the Lorentz Transformation as quickly as possible is a desirable goal. From there, one can then quickly deduce the basic 4D geometry of spacetime, which then leads to everything else.

In my judgement, before discussing the Lorentz Transformation, it is important for students to begin to develop awareness and comfort with some of the new phenomena they are going to encounter in SR. It doesn't have to be much; just enough to pique their interest. Any ideas on how to accomplish this?

As far as deriving the Lorentz Transformation is concerned, it leaves me cold to think that you might have in mind using Einstein's two postulates. These two postulates are, in my judgement, not the essence of SR. They are the effects of the unique 4D geometry of spacetime, and, although they are historically significant, are not the causes of anything. Did you have in mind deriving the Lorentz Transformation using something other than the 2 postulates?

Chet

 

[valentin mano]

Flat Spacetime does not mean "inertial frame of reference",which is the initial frame of Special Relativity.