Counter intuitivity and relativity

[Grimble]

One of the first expressions that I came across in studying SR was that it was Counter Intuitive.

In particular this expression was used to define the relationship between local time and the time measured by a 'moving clock'.

It seemed to be thought that newcomers to the theory would assume that, as the traveling clock would be seen to run slowly by a stationary observer, then an observer moving with the clock, would expect see the stationary clock run fast.

{But that would mean that the 'newcomer' would be imagining it all as a single frame of reference - (such as the clock in a moving car running fast compared to a stationary one, which would be true if that clock were, indeed, running fast)}.

But that is not what is being compared, is it?

Are we not comparing the measuring of a moving clock, compared with a stationary (local) one?

And, if so, then the reciprocal is measuring exactly the same measurement, i.e. the measurement of a clock (local to the stationary observer) moving relative to an observer local to the 'moving' clock.

So in each case it is the measurement of a clock moving relative to the observer making the measurement. So, at least to me, it is intuitive that the two measurements would show the same relationship.

This brings one to the question; if the two clocks are identical and the moving clock runs slow, which is the real time?

(And I suppose, the associated question; if something can be measured, is it there fore real?)

Now, my answer would be Yes they are real and therefore that both measurements have to be real.

But how can both measurements be 'real' if they are identical clocks showing different times?

The answer that I give has to be that both measurements are real and correct because they are not measuring the same thing.

It seems to be assumed that because we are dealing with clocks that are local to each of two frames of reference, and that because 'clocks' somehow define how we measure time in SR, that we are measuring the same interval.
But in one case we are measuring a stationary (local) clock and in the other we are measuring a moving clock. i.e. we are measuring it under different conditions.

Am I getting this right?

 

[Fredrik]

The answer that I give has to be that both measurements are real and correct because they are not measuring the same thing.

This is correct. A clock measures the proper time of the curve in spacetime that represents its motion. ("Proper time" is a coordinate independent mathematical property of a curve).

 

[tiny-tim]

Hi Grimble! Hi Fredrik!

… The answer that I give has to be that both measurements are real and correct because they are not measuring the same thing.

It seems to be assumed that because we are dealing with clocks that are local to each of two frames of reference, and that because 'clocks' somehow define how we measure time in SR, that we are measuring the same interval.
But in one case we are measuring a stationary (local) clock and in the other we are measuring a moving clock. i.e. we are measuring it under different conditions.

Am I getting this right?

This is correct. A clock measures the proper time of the curve in spacetime that represents its motion. ("Proper time" is a coordinate independent mathematical property of a curve).

ah, that's for a moving clock that turns round and comes back.

Isn't the question about two clocks that stay stationary in different inertial frames … how can each's measurement of the other as slow be real and correct?

I'd say that they are measuring the same thing (well, each other's same thing! ), since each is measuring a moving clock (not one stationary and one moving).

Grimble will have to look for another explanation as to how it can be real and correct that each measures the other as slow. ​

 

[JesseM]

Here's how I'd summarize the difference: If we want to measure the rate clock B is ticking in the rest frame of clock A, we can't just measure that using clock A itself, we need multiple synchronized clocks at rest in clock A's frame to compare their times with the time on B as it passes them. For example, if clock A reads 10 seconds and B reads 10 seconds at the moment they pass, and clock A2 (which is at rest relative to A, and synchronized with A in their own rest frame) reads 20 seconds and B reads 18 seconds when they pass one another, then we can say that B is only ticking at 0.8 the rate of A and A2 in their mutual rest frame.

On the other hand, if we want to measure the rate A is ticking in the rest frame of clock B, we have to do the reverse, using multiple clocks at rest and synchronized in B's frame, say B and B2. Then if A and B both read 10 seconds when they pass, but when A passes B2, A reads 18 seconds while B2 reads 20 seconds, then we can say that in the B rest frame it is clock A that is running slow by a factor of 0.8.

I provided I diagram illustrating such a scenario with multiple clocks moving alongside each other in this thread, if the above is unclear you may want to take a look.

 

[Fredrik]

ah, that's for a moving clock that turns round and comes back.

What I said is true for all (ideal) clocks in both SR and GR, but you're right about this:

Grimble will have to look for another explanation as to how it can be real and correct that each measures the other as slow. ​

An explanation should mention that the definition of what it means to measure the ticking rate of a distant clock as slow is that we determine that it advances less than ε seconds between two events on its world line that are simultaneous and ε seconds apart in our co-moving inertial frame. (At least this is the definition we'd use when both clocks are moving with constant velocity forever).

The reason why the "apparent conflict" isn't really a conflict is that my co-moving inertial frame isn't the same as yours. So if we just understand the basic definitions, it's not even an apparent conflict.

 

[Frame Dragger]

I don't find this conter-intuitive. Within the framework of the theory it's a natural conclusion, or it seems to be. Am I missing something? (I'm serious, am I?)

 

[tiny-tim]

I don't find this conter-intuitive.

uhh? "A is slower than B, and B is slower than A" not counter-intuitive?

What would Euclid have said?? ​

 

[Frame Dragger]

uhh? "A is slower than B, and B is slower than A" not counter-intuitive?

What would Euclid have said?? ​

Probably something that is a bannable offense! Then again, Euclid wasn't a Relativist! ;)

EDIT: Ok, it would be bannable if you spoke ancient greek. Fortunately I have the rare power to curse in modern and ancient greek... a power I shall not exercise. :laugh:

 

[Grimble]

Isn't the question about two clocks that stay stationary in different inertial frames … how can each's measurement of the other as slow be real and correct?

I'd say that they are measuring the same thing (well, each other's same thing! ), since each is measuring a moving clock (not one stationary and one moving).

Grimble will have to look for another explanation as to how it can be real and correct that each measures the other as slow. ​

Thank you, tiny-tim and Hi!

But that is exactly what I am saying!

But in one case we are measuring a stationary (local) clock and in the other we are measuring a moving clock. i.e. we are measuring it under different conditions.

so you are agreeing with my explanation, (but maybe I could have phrased it better).

 

[Dale]

if the two clocks are identical and the moving clock runs slow, which is the real time?

(And I suppose, the associated question; if something can be measured, is it there fore real?)

Now, my answer would be Yes they are real and therefore that both measurements have to be real.

But how can both measurements be 'real' if they are identical clocks showing different times?

I have yet to find a good definition of "real". Do you have one? If not then I would recommend staying away from all questions about the reality of something.

Time dilation is a frame varying measurable effect. Whether or not you want to call that real depends entirely on your definition of "real".

 

[Grimble]

I don't find this conter-intuitive. Within the framework of the theory it's a natural conclusion, or it seems to be. Am I missing something? (I'm serious, am I?)

Well I think you are right, because you are looking at it within the right framework.

My point was that to say it was counter intuitive is to belittle newcomers to the theory by implying that it is beyond them to understand what is being described.

 

[Frame Dragger]

Well I think you are right, because you are looking at it within the right framework.

My point was that to say it was counter intuitive is to belittle newcomers to the theory by implying that it is beyond them to understand what is being described.

Understood! I see your point.

DaleSpam Well... I think I'd argue for the reality of time dilation. Gravitational lensing has been directly observed, and many other properties that would be terribly inconsistant if GR was wrong. The consintancy of the observation of the laws of physics is only maintained if effects such as time dilation are real. By real, I would say it's something you and I experience daily. Astronauts experience it, and a clock on an airplane did. That's real for me.

If we lived in a purely GR world, I think you could make a good argument for local realism. the fact that QM is telling us that is not the whole story is valid, but outside of the purview of the intuitivite nature of Relativity.

 

[Dale]

By real, I would say it's something you and I experience daily.

I also experience dreams daily. According to that definition dreams are real. Is that what you want?

 

[Frame Dragger]

I also experience dreams daily. According to that definition dreams are real. Is that what you want?

Dreams are real, your subjective interpretation of that neurological activity during sleep or upon waking is only real as a subjective experience. However in theory each neuron's activity could be mapped, so yes, dreams are as real as sleep.

The pink elephant you rode in the dream, is not real, that is the definition of a 'fantasy'.

I think people have the semantic BALLS, to make distinctions between 'real' experiences, and the subjective experience of one person that is not universally observed to be consistant.

This is the Relativity area after all, and we're not talking about $$\Psi = \infty$$ of pure SQM. (to be clear, I mean 'the wavefunction is everything' not literally psi at infinity)

 

[tiny-tim]

I also experience dreams daily. According to that definition dreams are real. Is that what you want?

I experience dreams nightly!

But in one case we are measuring a stationary (local) clock and in the other we are measuring a moving clock. i.e. we are measuring it under different conditions.

so you are agreeing with my explanation, (but maybe I could have phrased it better).

No, sorry , I'm completely disagreeing …

you're saying that two "inertial clocks" are different, because one is stationary and the other is moving, and that that difference explains the apparently counter-intuitiveness …

I'm saying they're exactly the same, and you'll have to look for another explanation.

 

[Mentz114]

I think I'd argue for the reality of time dilation. Gravitational lensing has been directly observed, and many other properties that would be terribly inconsistant if GR was wrong. The consintancy of the observation of the laws of physics is only maintained if effects such as time dilation are real. By real, I would say it's something you and I experience daily. Astronauts experience it, and a clock on an airplane did. That's real for me.

That is not time dilation, it's differential ageing. And it has nothing to do with lensing.

Time dilation is a frame varying measurable effect. Whether or not you want to call that real depends entirely on your definition of "real".

I emphatically agree.

 

[Dale]

Dreams are real, your subjective interpretation of that neurological activity during sleep or upon waking is only real as a subjective experience. However in theory each neuron's activity could be mapped, so yes, dreams are as real as sleep.

OK, I will certainly agree that neurological activity is mappable (or measurable), but that is not a part of your definition of "real".

The pink elephant you rode in the dream, is not real, that is the definition of a 'fantasy'.

I certainly experienced it. According to your definition that makes it "real".

My point is that it is notoriously difficult to come up with a good definition of "real". The definition "something you and I experience daily" has lots of holes in it. For example, what about something that is real but rare? It would not meet your definition since it may not be experienced daily. What about something like love that is immaterial but a common experience, do you want to classify that as "real" or not? What about something that is physical and can be measured but not experienced directly, what types of experiences qualify something for reality?

I am not trying to be annoying here, it is just that I feel it is pointless to discuss of whether or not something is "real" until the term is defined clearly. There is a whole branch of philosophy, ontology, devoted to this topic. It is not trivial (although it is probably not important either).

 

[Frame Dragger]

That is not time dilation, it's differential ageing. And it has nothing to do with lensing.


I emphatically agree.

I was talking about situations in which confirmation of GR's predictions have been tested.

 

[Frame Dragger]

OK, I will certainly agree that neurological activity is mappable (or measurable), but that is not a part of your definition of "real".

I certainly experienced it. According to your definition that makes it "real".

My point is that it is notoriously difficult to come up with a good definition of "real". The definition "something you and I experience daily" has lots of holes in it. For example, what about something that is real but rare? It would not meet your definition since it may not be experienced daily. What about something like love that is immaterial but a common experience, do you want to classify that as "real" or not? What about something that is physical and can be measured but not experienced directly, what types of experiences qualify something for reality?

I am not trying to be annoying here, it is just that I feel it is pointless to discuss of whether or not something is "real" until the term is defined clearly. There is a whole branch of philosophy, ontology, devoted to this topic. It is not trivial (although it is probably not important either).

You're not being annoying, but without getting into overly philosophical realms... you never did ride that pink elephant. You THOUGHT you did, but not even in the complete manner of a normal 'thought'. I agree that 'something you and I experience daily' can't be the only standard of 'real', but then that was not a very good expression of what I meant.

As for discussing what is real, there is probably never going to be a point in our lives (or any others) when that is a question which can absolutely be answered. That said, when people toss 'love' and 'dreams' my way, I find that glib. Love is entirely explicable as yet another biological process, where the angst and complexity arises from the humnan interpretation. My point? When people talk to each other they always establish de facto conventions of speach, and I believe without quibbling that we don't need to discuss the potential reality of love and dreams.

I'm talking about The Casimir Effect vs. the existence of Pions. The Lens-Thirring Effect, Gravitational lensing, Differential Aging, and all of the other notions derived from Relativity vs. The Higg's Mechanism, Photon Decay, etc.

To be blunt, I'm talking about a simple consensus based on empirical evidence, vs just the kind of immaterial speculation of 'love'.

You CAN try to use language in a manner consistant with math, with rigor and commonly agreed conventions at each point for a given model. The fact that most people can't and DON't isn't my damned fault.

 

[Mentz114]

... is only maintained if effects such as time dilation are real. By real, I would say it's something you and I experience daily. Astronauts experience it, and a clock on an airplane did.

The experiments with clocks on planes are not testing time dilation. Time dilation is the apparently paradoxical ( and counter-intuitive) prediction of the LT that two IFRs will see each others clocks running slower.

 

[Dale]

without getting into overly philosophical realms ... I believe without quibbling that we don't need to discuss the potential reality of love and dreams.

I agree with this.

In general, the only way to resolve any question of the form "Is X Y?" is to check the properties of X against the definition of Y. Because the definition of "real" is so difficult it makes the question "Is X real?" inherently difficult to answer regardless of X.

Yes, as you pointed out, we do have "de facto conventions of speach" and "a simple consensus based on empirical evidence" for the reality of everyday things like rocks and dream-elephants; we agree that whatever the definition of real is it should apply to rocks and not to dream-elephants.

But what about time dilation? There is no such de facto convention to rely on and so we have to examine the properties of time dilation and check how they mesh with the idea of "real". One property of time dilation is that it is measurable, another is that it is frame-variant. Unfortunately, the de facto conventions tend to suggest that measurable things are real and frame-variant things are not real (at least I can see the rationale for each stance).

So we are left again with the need for a good definition of "real". Until we have such a definition I feel that it is best to simply enumerate the properties that time dilation has and avoid ambiguous questions of sematics.

 

[Frame Dragger]

The experiments with clocks on planes are not testing time dilation. Time dilation is the apparently paradoxical ( and counter-intuitive) prediction of the LT that two IFRs will see each others clocks running slower.

Sorry, I'd say I'm tired, but the truth is that was just a brain-spasm. I will drill it into my brain... differential aging... differential aging... save TD for the Twin Paradox... *smacks self*

I agree with this.

In general, the only way to resolve any question of the form "Is X Y?" is to check the properties of X against the definition of Y. Because the definition of "real" is so difficult it makes the question "Is X real?" inherently difficult to answer regardless of X.

Yes, as you pointed out, we do have "de facto conventions of speach" and "a simple consensus based on empirical evidence" for the reality of everyday things like rocks and dream-elephants; we agree that whatever the definition of real is it should apply to rocks and not to dream-elephants.

But what about time dilation? There is no such de facto convention to rely on and so we have to examine the properties of time dilation and check how they mesh with the idea of "real". One property of time dilation is that it is measurable, another is that it is frame-variant. Unfortunately, the de facto conventions tend to suggest that measurable things are real and frame-variant things are not real (at least I can see the rationale for each stance).

So we are left again with the need for a good definition of "real". Until we have such a definition I feel that it is best to simply enumerate the properties that time dilation has and avoid ambiguous questions of sematics.

I accept your point as valid, but my own view is a little different. If Time Dilation doesn't have a 'real' (in the conventional sense) effect for the travelers in different frames, that strikes me as a rejection of basic tenents of Relativity. The same can be said for Differential Aging; what could be more 'real' than returning from your 3 hour tour to find that time had passed differently (from your perspective) at your starting point!

If you argue that wouldn't be the result of a relativistic round trip, I would beg to differ.

As for Time Dilation, the answer HAS to be that both points of view are real. They are equally valid descriptions of reality, from the relative intertial frames. More than one thing can be real, and the 'inherent contradiction' is simply an artifact. Someday we may perform the test with real twins in real near-c 'ships'. Who knows. If that is done, real people and ships will experience real contrasts with their twin. It won't be something that Depak Chopra can wave away, nor is it a rideable pink pachyderm. I consider that realistic, and real. It's not probabilistic and 'smeared' in a way we're incapable of visualizing, and thus rely on approximations and models that tell us about a world we can't see or recognize.

If my namesake is real, Time Dilation is real. Inertial frames, however you describe them, contain valid clocks. All clocks are valid assuming the theory is correct, and I'm not about to say it isn't. Again, that seems real and intuitive. A little strange, but then, we are bathed in aprx 7 minute old light and it doesn't seem to bother us, and that's a bit werid too when you first learn what that means.

 

[Dale]

I accept your point as valid, but my own view is a little different. If Time Dilation doesn't have a 'real' (in the conventional sense) effect for the travelers in different frames

What is the conventional sense as applied to time dilation? This isn't something as concrete as cement nor as fantastic as a dream. It is hard for me to see how the "conventional sense" can be applied at all here.

The same can be said for Differential Aging; what could be more 'real' than returning from your 3 hour tour to find that time had passed differently (from your perspective) at your starting point!

Well, differential aging is much less problematic reality-wise. Differential aging is measurable and frame-invariant, which are both good candidate attributes for real things. Most (non-crackpot) proponents of the "unreal time dilation" position take the stance that all of the experimental results that you might use to justify the reality of time dilation can be expressed purely in terms of proper time which (being measurable and frame invariant) is the real thing. They generally further point out that time dilation requires some synchronization convention which is obviously just a convention and has no more bearing on reality than any other convention.

Someday we may perform the test with real twins in real near-c 'ships'. Who knows. If that is done, real people and ships will experience real contrasts with their twin.

I don't think we need to wait for that. The evidence with muons in storage rings is quite clear and convincing. The question of the reality of time dilation is not one of evidence, the evidence is in and clearly supports SR. The question of the reality of time dilation is simply a semantic question.

 

[Frame Dragger]

What is the conventional sense as applied to time dilation? This isn't something as concrete as cement nor as fantastic as a dream. It is hard for me to see how the "conventional sense" can be applied at all here.

Well, differential aging is much less problematic reality-wise. Differential aging is measurable and frame-invariant, which are both good candidate attributes for real things. Most (non-crackpot) proponents of the "unreal time dilation" position take the stance that all of the experimental results that you might use to justify the reality of time dilation can be expressed purely in terms of proper time which (being measurable and frame invariant) is the real thing. They generally further point out that time dilation requires some synchronization convention which is obviously just a convention and has no more bearing on reality than any other convention.

I don't think we need to wait for that. The evidence with muons in storage rings is quite clear and convincing. The question of the reality of time dilation is not one of evidence, the evidence is in and clearly supports SR. The question of the reality of time dilation is simply a semantic question.

I believe I need to think more about this, and read more. I seem to have an unexpected (to me only I'm sure lol) weakness in an area I used to be familiar with. You last point especially is one that I COULD argue with if I didn't completely agree with it.

Thanks to both DaleSpam and Mentz114 for correcting me in my error.

 

[Grimble]

No, sorry , I'm completely disagreeing …

you're saying that two "inertial clocks" are different, because one is stationary and the other is moving, and that that difference explains the apparently counter-intuitiveness …

I'm saying they're exactly the same, and you'll have to look for another explanation.

I'm sorry, but we do seem to be getting at cross purposes here

Langauge can be very difficult sometimes, we read the same words but, possibly using different emphasis and rhythms of speech, we understand a completely different meaning.

I will try again to clarify what I mean...

I am not saying the two clocks are different, I am saying they are exactly the same.
Each clock, observed locally, will read the same time.
Each clock, observed remotely, will read the same as the other, observed remotely.

What I am saying is that the same clock will indicate a different time, depending on whether that one clock is viewed locally or remotely.
I am saying that the difference is due to the way the clock is viewed, the conditions under which it is viewed; and, hence, that the same effect will apply to each of the two clocks. So the fact, that each will see the moving clock read less, follows...

 

[tiny-tim]

What I am saying is that the same clock will indicate a different time, depending on whether that one clock is viewed locally or remotely.
I am saying that the difference is due to the way the clock is viewed, the conditions under which it is viewed; and, hence, that the same effect will apply to each of the two clocks. So the fact, that each will see the moving clock read less, follows...

ah, in that case I agree …

but I don't see how that explains the counter-intuitiveness (ie how B can be slower than A if A is slower than B).

 

[Ich]

but I don't see how that explains the counter-intuitiveness (ie how B can be slower than A if A is slower than B).

Because, if properly worded, it would mean: A>B while C>D. There's no "slower" or "faster" in the first place, there are four different spacetime intervals that follow said inequalities. The prblem arises if one uses one and the same word for A and D, or B and C respectively.

 

[Grimble]

ah, in that case I agree …

but I don't see how that explains the counter-intuitiveness (ie how B can be slower than A if A is slower than B).

In each case the time viewed remotely is less than the time viewed locally, so it is the conditions under which it is viewed (moving as opposed to stationary) that are affecting the measurement taken.

AND, because the difference is a function of their relative velocity, it fits nicely (to me at least) that it is an effect of that relative velocity...

 

[Rasalhague]

My point was that to say it was counter intuitive is to belittle newcomers to the theory by implying that it is beyond them to understand what is being described.

If I've ever used the word counterintuitive in our discussions here (and I'm sure I must have!), it certainly wasn't meant to belittle anybody. Quite the opposite. I wanted to express sympathy at someone else struggling with concepts that's I've struggled with too.

The idea that the "most direct route" through spacetime is the longest (measured as proper time), while the "most round-about route" is the shortest isn't what you'd immediately expect after being told that time is a dimension, a bit like the dimensions of space; it goes against a basic instinct we all have about space. The idea that there's no natural way to define a frame-independent universal "now" (any more than we can define a frame-independent universal "here") is so counterintuitive, I remember watching that animation from The Mechanical Universe again and again... We have no context for such a statement in our everyday lives; on first meeting it, you wonder not just what it means, but what it could possibly mean.

On the other hand, I also remember, before I found a basic mathematical treatment of SR, reading popular science books or seeing TV programmes that went on about how weird this all is, illustrating it's supposed weirdness with what seemed like outright contradictions (clocks that each run slow from the other's "perspective"), as if to suggest that it's actually our dislike of contradiction that's the intuition we need to overcome! It was much more fun to learn the even weirder but perfectly logical way that paradox is resolved.

 

[Grimble]

If I've ever used the word counterintuitive in our discussions here (and I'm sure I must have!), it certainly wasn't meant to belittle anybody. Quite the opposite. I wanted to express sympathy at someone else struggling with concepts that's I've struggled with too.

Yes, that is quite valid too, I was not meaning to imply that everyone was 'belittling' the newcomer, only that some were, by overusing that phrase.

The idea that the "most direct route" through spacetime is the longest (measured as proper time), while the "most round-about route" is the shortest isn't what you'd immediately expect after being told that time is a dimension, a bit like the dimensions of space; it goes against a basic instinct we all have about space. The idea that there's no natural way to define a frame-independent universal "now" (any more than we can define a frame-independent universal "here") is so counterintuitive, I remember watching that animation from The Mechanical Universe again and again... We have no context for such a statement in our everyday lives; on first meeting it, you wonder not just what it means, but what it could possibly mean.

And what you are describing here could certainly be decribed that way.
But the way, I, and presumably many more students of SR (and even of science generally), tend to look at such things; is that that is why we are here in the first place. We are looking to find the explanation, the logic of how things work that will enable us to see initially 'counter-intuitive' aspects of physics become 'intuitive'.

After all, isn't something 'counter-intuitive' only when it is outside our experience?

On the other hand, I also remember, before I found a basic mathematical treatment of SR, reading popular science books or seeing TV programmes that went on about how weird this all is, illustrating it's supposed weirdness with what seemed like outright contradictions (clocks that each run slow from the other's "perspective"), as if to suggest that it's actually our dislike of contradiction that's the intuition we need to overcome! It was much more fun to learn the even weirder but perfectly logical way that paradox is resolved.

Yes indeed, we must be thankful we no longer put anything we don't understand down to 'magic'! (or Aliens, I suppose)