Do the Principles of Special Relativity Require Synchronized Clocks in K and k?

[JM]

No. The clocks of K are in synch with each other. The clocks of k are in synch with each other. ".

All the clocks of K and k start at 0 when the origins coincide ( point 2) and all advance at the same rate ( point 3). Isn't this 'in synch?'

 

[Dale]

All the clocks of K and k start at 0 when the origins coincide ( point 2) and all advance at the same rate ( point 3). Isn't this 'in synch?'

No, because the phrase "when the origins coincide" refers to two separate sets of events for k and K. Also although you can say that they "advance at the same rate" they also "advance in different directions (in spacetime)" so even if you de-synchronized all of the clocks in k such that the first statement is true in K that would not imply that they would remain in sync in K. There is no sense in which "all the clocks of both K and k are in sync".

 

[JM]

. Similarly, if we have one clock measure a vertical line through spacetime (at rest) and another clock measure a diagonal line through spacetime (in motion) then we will find that the measurements differ by a factor of $\gamma$. We again attribute this difference to a difference in the thing being measured instead of to the clocks, since they are identical.

DaleSpam,
Where do we stand now? You seem to agree with my statement of the properties of clocks, in your posts 27, 29, and 33. In addition you have offered in post 33 the example given above.

This example expresses the point I’m trying to make in this thread. The properties presented in post 1 are intended to indicate that the SR clocks are identical. Thus, as you say, the time dilation equation represents the difference in the thing being measured, which is the propagation of light. Thus the common expression that ‘moving clocks run slow’ is not literally correct, and clocks don’t change their behavior due to motion. And the apparent change of tick rate seen when one observer looks at another’s clocks is due to the properties of light, as affected by the postulate of constant light speed.
Are we agreed on this?
However, your last post 37 seems to be disagreeing with something, but I’m not sure what. Is it my use of the term ‘synch’ instead of ‘identical’. Do you want to explain your comments further?

Thanks for your inputs.
JM

 

[Dale]

However, your last post 37 seems to be disagreeing with something, but I’m not sure what. Is it my use of the term ‘synch’ instead of ‘identical’.

I thought that I was pretty clear in multiple posts that what I was objecting to is your statement that "all the clocks of both K and k are in sync". There is no sense in which that is true, and "identical" is not a synonym for "synch". Two identical clocks may not be synchronized and two synchronized clocks may not be identical.

"Identical" means that they are physically constructed the same and operate the same, as described above. "Synchronized" means that they have some agreed upon procedure for comparing their displayed time and that when they do so they get the same result. In relativity the standard procedure for comparing clock times is called the Einstein synchronization convention. Under that convention the clocks of K are synchronized with each other and the clocks of k are synchronized with each other, but the clocks of K are not synchronized with the clocks of k.

I don't know how I can possibly be more clear than this.

 

[Al68]

I gather that you agree that T and t must be expressed in the same units. What that means is that the clocks used to measure T and t must tick at the same rate...

No, it doesn't mean that at all. Same units doesn't mean same rate any more than the fact that the same units are used for velocity means that the velocity of a specific clock is the same in K as in k. Relative velocity is a frame dependent quantity, so it has a different value in K than in k for each clock. Relative tick rate is also frame dependent.

Many quantities, even in classical physics, are frame dependent, and so have different values in different reference frames. Examples are momentum and kinetic energy. The kinetic energy of a specific clock has a different value in K than in k, although the same units are used. Ditto for momentum and tick rate.

Thus the common expression that ‘moving clocks run slow’ is not literally correct, and clocks don’t change their behavior due to motion.

Of course clocks don't change their behavior due to motion. That's a common misconception of SR.

The relative velocity of a car has a different value relative to different observers. It's not because the car "changed its behavior". It's a single car observed by different observers, so the values for velocity, kinetic energy, momentum, etc are different because, like the tick rate of a clock, those quantities are frame dependent.

 

[JM]

I thought that I was pretty clear in multiple posts that what I was objecting to is your statement that "all the clocks of both K and k are in sync". There is no sense in which that is true, and "identical" is not a synonym for "synch". Two identical clocks may not be synchronized and two synchronized clocks may not be identical.

"Identical" means that they are physically constructed the same and operate the same, as described above. "Synchronized" means that they have some agreed upon procedure for comparing their displayed time and that when they do so they get the same result. In relativity the standard procedure for comparing clock times is called the Einstein synchronization convention. Under that convention the clocks of K are synchronized with each other and the clocks of k are synchronized with each other, but the clocks of K are not synchronized with the clocks of k.

I don't know how I can possibly be more clear than this.

I accept your comments as subjects for further discussion.
In the meantime, let me ask:
Isn't it a fundamental principle of physics equations that all terms in an equation must be expressed in the same units?
If so, isn't it required that T and t in the equation t = T/gamma must be expressed in the same units?
Doesn't that require that t and T not only have the same name, e.g. seconds, but also that the seconds must be the same size for both?
JM

 

[JM]

Of course clocks don't change their behavior due to motion. That's a common misconception of SR.

Hello, Al68. So, do you agree with the statement that ' the common expression that 'moving clocks run slow' is not literally correct'?

 

[JesseM]

Hello, Al68. So, do you agree with the statement that ' the common expression that 'moving clocks run slow' is not literally correct'?

It depends whether you define "rate of ticking" as a "behavior", doesn't it? I think Al68's point was that rate of ticking is one of a number of quantities which are inherently frame-dependent, just like momentum or velocity. "Moving clocks run slow" is literally correct in the same sense that "faster-moving 1-kilogram masses have a greater momentum" is literally correct, but the latter doesn't imply the 1-kilogram masses "change their behavior due to motion", if "behavior" is defined solely in frame-invariant terms.

 

[Dale]

I accept your comments as subjects for further discussion.
In the meantime, let me ask:
Isn't it a fundamental principle of physics equations that all terms in an equation must be expressed in the same units?
If so, isn't it required that T and t in the equation t = T/gamma must be expressed in the same units?
Doesn't that require that t and T not only have the same name, e.g. seconds, but also that the seconds must be the same size for both?

Yes, I already said so in post 33.

Similarly, if b is the base of a right triangle and h is the hypotenuse then $b = h \; cos(\theta)$ is only true if b and h have the same units. Before asking your next question please think about that equation a bit and how it relates to what we have been discussing.

 

[Al68]

Hello, Al68. So, do you agree with the statement that ' the common expression that 'moving clocks run slow' is not literally correct'?

A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.

The moving clock runs slower because its tick rate depends on relative velocity, and therefore frame of reference, not because it physically changed in any way.

It's analogous to the fact that a baseball, after being thrown forward from a moving truck, will have greater velocity in the reference frame of the ground than in the reference frame of the truck. It's the same baseball. Nothing about the baseball physically changes because we choose to compare its velocity to the truck instead of the ground. It isn't moving slower relative to the truck because it "slowed down", it's because velocity is frame dependent. So is the tick rate of clocks.

 

[JesseM]

A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.

Are you arguing that "tick rate" can be defined in a frame-invariant way? It seems to me that "tick rate" always means "rate of ticking relative to coordinate time in some frame", I don't see how you could meaningfully define it relative to proper time (since the number of ticks along a worldline defines the proper time along that worldline) or any other frame-invariant quantity. If "tick rate" is an inherently frame-dependent notion then clocks do change their tick rates just like they change their velocities or momenta or x-coordinate.

 

[matheinste]

To anyone.

Given two identical clocks in relatively moving inertial frames, one clock at rest in each, and given that the laws of physics are the same in all inertial frames, can we not in any meaningfully way ask if the two clocks tick at the same rate although we are unable to directly compare them side by side.

Matheinste.

 

[Dale]

Given two identical clocks in relatively moving inertial frames, one clock at rest in each, and given that the laws of physics are the same in all inertial frames, can we not in any meaningfully way ask if the two clocks tick at the same rate although we are unable to directly compare them side by side.

Sure, all you have to do is operationally define "tick rate". For example, you may define "tick rate" by comparison to some co-moving reference standards (in which case the tick rates would be the same). Or you may define "tick rate" by comparison to some single reference standard using a given simultaneity convention (in which case the tick rates would be different).

 

[matheinste]

Sure, all you have to do is operationally define "tick rate". For example, you may define "tick rate" by comparison to some co-moving reference standards (in which case the tick rates would be the same). Or you may define "tick rate" by comparison to some single reference standard using a given simultaneity convention (in which case the tick rates would be different).

So what can I say about the clock rates if the Lorentz transformed time unit from an inertial reference frame moving relative to me equals my time unit. I would say they are the same but after some comments in this thread I am not sure if it means anything.

Does it all come down to the behaviour of reference standards in relatively moving frames. If they are equal by definition, what does the definition mean by equal.

These points may seem trivial to many but they are fundamental to me.

Matheinste.

 

[Al68]

A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.

Are you arguing that "tick rate" can be defined in a frame-invariant way? It seems to me that "tick rate" always means "rate of ticking relative to coordinate time in some frame", I don't see how you could meaningfully define it relative to proper time (since the number of ticks along a worldline defines the proper time along that worldline) or any other frame-invariant quantity. If "tick rate" is an inherently frame-dependent notion then clocks do change their tick rates just like they change their velocities or momenta or x-coordinate.

The statement "clocks do change their tick rates" misleadingly attributes the difference in its tick rate in different frames to an action performed by or to the clock.

If one measures the speed of a car relative to the ground, then measures the speed of the same car relative to another car, we wouldn't say the car "slowed down". Saying that the car slowed down would be inaccurate and misleading. It would prompt questions like: "what caused the car to slow down?"

 

[Academic]

I'm not so sure about that. Suppose you have a train of length L traveling speed v to the right. If two beams of light are emitted from either end of the train, at the same time according to the train's reference frame, then they will arrive at the center of the train at the same time according to the train's reference frame. But if I'm not mistaken, according to an observer on the ground they will have arrived at the center of the train at different times. Correct me if I'm wrong, though, since I haven't really studied special relativity in great detail. What I know comes mainly from popular books, which can be misleading.

Hes saying its not like the train, because in the train the beams are at different locations. If you have two clocks at the same time and at the same location there is no relativity of simultaneity to worry about. Only when they are separated does that become an issue (and the more separated they are the more of an issue it is)

 

[JesseM]

The statement "clocks do change their tick rates" misleadingly attributes the difference in its tick rate in different frames to an action performed by or to the clock.

If one measures the speed of a car relative to the ground, then measures the speed of the same car relative to another car, we wouldn't say the car "slowed down". Saying that the car slowed down would be inaccurate and misleading. It would prompt questions like: "what caused the car to slow down?"

But when people say "cars can change their velocities" they're not talking about measuring the speed of a single inertial car from the perspective of two different frames, they're talking about measuring the velocity of a car before and after it accelerates, as seen in a single inertial frame. Similarly if someone says "clocks do change their tick rates" the normal context would be talking about a clock that accelerates (or multiple identically-constructed clocks moving at different velocities) as seen in a single inertial frame; from the perspective of this single frame, the frame-dependent quantity "rate of ticking" does change.

 

[Al68]

But when people say "cars can change their velocities" they're not talking about measuring the speed of a single inertial car from the perspective of two different frames, they're talking about measuring the velocity of a car before and after it accelerates, as seen in a single inertial frame. Similarly if someone says "clocks do change their tick rates" the normal context would be talking about a clock that accelerates (or multiple identically-constructed clocks moving at different velocities) as seen in a single inertial frame; from the perspective of this single frame, the frame-dependent quantity "rate of ticking" does change.

Sorry, I misunderstood your post. I was referring to the statement that a "moving clock runs slow", which I took to mean a clock in inertial motion running slower in a different reference frame than the one in which it is at rest.

For a clock that accelerates, I agree, the change in tick rate relative to its initial rest frame is (indirectly) caused by an action performed on the clock.

 

[JM]

A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.

These two statements seem contradictory to me. In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.
To resolve this I recognize a difference between the properties of clocks and the properties of light. The properties of clocks discussed in this thread suggest to me that the clocks of K and k 'tick' at the same rate. There seems to be various comments that support this idea. If the clocks all start at zero when the origins coincide then all the clocks read the same.
The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this. But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?

 

[JesseM]

But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?

If you have some set of equations defining how particles/fields/etc. behave in one inertial coordinate system, like Maxwell's laws of electromagnetism, it is a purely mathematical question as to whether these equations are "Lorentz-symmetric", with Lorentz-symmetry meaning that if you describe the motions of the same particles/fields/etc. using a different inertial coordinate system obtained by doing a Lorentz transformation on the first coordinate system, the exact same set of equations will accurately describe their behavior in the second coordinate system. If all the underlying laws of physics governing the motions of the parts of a clock are Lorentz-symmetric, that is enough to guarantee that identically-constructed clocks at rest in different Lorentzian coordinate systems will each tick at the same rate relative to coordinate time in their own respective rest frames, which necessarily implies that each clock seems to be running slow in the other clock's rest frame.

So far, all the fundamental laws of physics we have found do indeed obey Lorentz-symmetric equations, including ones that describe things other than light, like the nuclear force in atoms.

 

[Dale]

These two statements seem contradictory to me.

They are not contradictory

In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.

And what does "relative to a stationary clock in a specified reference frame" mean in ordinary language? It is an important part of the sentence which you have neglected.

If the clocks all start at zero when the origins coincide then all the clocks read the same.

This is not correct. We have been over this before (e.g. post 37). You are going in circles.

The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this. But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?

The experimental support for the Lorentz transforms is overwhelming, and includes the dilation of clocks whose mechanism is not based on light, such as the half-life of unstable particles. The important thing about the Lorentz transforms is that there is a speed which is invariant. The fact that light travels at the invariant speed is essentially a coincidence due to the photon being massless. If the photon were eventually discovered to have some very small non-zero mass then light would not travel at exactly c. However, all of the experimental results confirming time dilation etc. would still be valid as would the Lorentz transform and SR with very minor changes to the wording of the second postulate.

 

[Al68]

A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.

These two statements seem contradictory to me. In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.

A moving clock does not "run slow" in this "ordinary language" sense. It runs slow only in a relative sense, ie relative to a "stationary clock". Clocks in SR are assumed to be working properly and each keeping perfect proper time.

The properties of clocks discussed in this thread suggest to me that the clocks of K and k 'tick' at the same rate.

In K, the clock of k runs slower than the clock of K. In k, the clock of K runs slower than the clock of k. In neither frame do the clocks run at the same rate, unless there is no relative motion between them.

The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this.

He didn't "blame the clocks" for anything. He assumed perfectly working clocks that each kept proper time. He attributed the difference to the fact that time itself passes at a different rate relative to different reference frames.

So I think that t<T is the fault of the light not the clocks.

It's related to the speed of light being constant, yes. The clocks are each just keeping proper time.

 

[JM]

other[/i] clock's rest frame.
..

I note that you say "seems to be running slow..' Does that refer to the relation t=T/gamma? If so, do you think that the apparent slowness is due to the properties of the clocks or due to the properties of the light?
Have you published on SR? If not, where have you gotten your knowledge? I have read everything I could find, and found no real explanations.

 

[Al68]

I note that you say "seems to be running slow..' Does that refer to the relation t=T/gamma? If so, do you think that the apparent slowness is due to the properties of the clocks or due to the properties of the light?
Have you published on SR? If not, where have you gotten your knowledge? I have read everything I could find, and found no real explanations.

Einstein's original 1905 paper can be found here: http://www.fourmilab.ch/etexts/einstein/specrel/www/

The reason for the relationship t=T/gamma is explained fully in this paper, and only requires a basic understanding of Newtonian physics.

The relation t=T/gamma is, like you say, not due to the properties of the clocks. The only relevant property of the clocks is that they are assumed to keep proper time.

 

[lugita15]

A moving clock certainly 'runs slow' relative to a stationary clock in a specified reference frame. But neither clock 'changed its tick rate' in any sense.

These two statements seem contradictory to me. In ordinary language to say a clock 'runs slow' means that something has happened to the clock ( the mainspring has run down, or the battery is low), and the clock has changed its 'tick rate' and no longer keeps the correct time.
To resolve this I recognize a difference between the properties of clocks and the properties of light. The properties of clocks discussed in this thread suggest to me that the clocks of K and k 'tick' at the same rate. There seems to be various comments that support this idea. If the clocks all start at zero when the origins coincide then all the clocks read the same.
The idea that clocks run slow is based on the Lorentz transforms. Insert X = v T and the result is t = T/gamma, i.e. t is less than T. Einstein blames the clocks for this. But the LT are based on the properties of light. Look where he starts to formulate, he says 'let a light ray emit at the common origin, be reflected and return. So I think that t<T is the fault of the light not the clocks.
OK?

No, not OK. The fact that t<T is neither the fault of light nor the fault of the clocks. It is the fault of time. Time is not an absolute concept that is the same for all observers. If you take two clocks that were made identically, then they will disagree about the duration of events if they happen to be moving at different speeds. The clocks are not malfunctioning, and light is not involved. Einstein mentions his procedure of using light beams, but this is a red herring. There he talks about using light beams only because the speed of light is the same for all observers. The time dilation phenomenon would be observed even if the observers used any other kind of particle to make their observations. The fact that people are using light to make observations makes their lives easier, but by no means is it necessary.

I thought this was already explained to you, but you keep reiterating your old points.

 

[JesseM]

I note that you say "seems to be running slow..' Does that refer to the relation t=T/gamma?

Yes, I'm referring to the ratio between elapsed time on the clock and coordinate time in a particular inertial frame.

If so, do you think that the apparent slowness is due to the properties of the clocks or due to the properties of the light?

It's due to the properties of the laws of physics (Lorentz-symmetry, which I mentioned above--any comments/questions about that post?), which govern the behavior of all physical systems, clocks and light included.

Have you published on SR? If not, where have you gotten your knowledge?

Haven't published, my knowledge comes from majoring in physics as an undergrad and doing my own reading on various physics-related subjects since then.

 

[DrGreg]

JM,

There is an analogy to be made between clocks measuring time and rulers measuring distance. Consider the diagram below. Do the two rulers both measure distance in the same way? The two rulers are both "synchronised" at their zero marks. Are they still synchronised at their "7" marks? Do they both measure "at the same rate"? Does one measure more distance than the other?

For instance, the blue lines seem to indicate that 5 blue units are equal to 5½ red units. On the other hand, the red lines seem to indicate that 5 red units are equal to 5½ blue units.

So is the red ruler "running short" compared to the blue ruler? Is the blue ruler "running short" compared to the red ruler?

You might think this example has little to do with clocks and time. But if you look at the mathematics behind my example and compare it with the mathematics behind Lorentz transforms and relativity, you will find that the two cases are really quite similar.

 

[yuiop]

I'm not so sure about that. Suppose you have a train of length L traveling speed v to the right. If two beams of light are emitted from either end of the train, at the same time according to the train's reference frame, then they will arrive at the center of the train at the same time according to the train's reference frame. But if I'm not mistaken, according to an observer on the ground they will have arrived at the center of the train at different times. Correct me if I'm wrong, though, since I haven't really studied special relativity in great detail. What I know comes mainly from popular books, which can be misleading.

Hi lugita, I am sorry, but do have to correct you. If two beams of light arrive at the center of the train at the same time according to the train's reference frame, then they do arrive at the same time in any reference frame. This is called an "event" and is frame invariant. Imagine a sensor at the centre of the train that triggers a bomb if both signals arrive at the same time. You can not have the bomb exploding and destroying the train according to an observer on the train and the bomb not exploding and continuing as normal according to an observer on the trackside.

 

[Aaron_Shaw]

Hi lugita, I am sorry, but do have to correct you. If two beams of light arrive at the center of the train at the same time according to the train's reference frame, then they do arrive at the same time in any reference frame. This is called an "event" and is frame invariant. Imagine a sensor at the centre of the train that triggers a bomb if both signals arrive at the same time. You can not have the bomb exploding and destroying the train according to an observer on the train and the bomb not exploding and continuing as normal according to an observer on the trackside.

So... this means that infact that, according to the observer, the light from the rear of the train is emitted before the light from the front, and so they both meet in the middle. Meanwhile from the mving train frame, both are emmitted at the same time and therefore meet in the middle also.

Either way they both meet in the middle because differences in opinion regarding the simultaneity of events means that the observer sees light emitted at different times from front and rear.

I understand how it could be confusing though, having watched the youtube vids, etc.
The train-and-platform thought experiment on wikipedia under 'relativity of simultaneity' show this, but it's the other way round. Light is emmitted from the center and hits the walls at different times. You can't just flip it round and assume that the light is emmitted 'simultaneously' in both frames because from the observing frame each point of emmission is separated by a distance and is moving. If it was simultaneous from the observing frame, then it must NOT be simultaneous from the train frame.

 

[lugita15]

Hi lugita, I am sorry, but do have to correct you. If two beams of light arrive at the center of the train at the same time according to the train's reference frame, then they do arrive at the same time in any reference frame. This is called an "event" and is frame invariant. Imagine a sensor at the centre of the train that triggers a bomb if both signals arrive at the same time. You can not have the bomb exploding and destroying the train according to an observer on the train and the bomb not exploding and continuing as normal according to an observer on the trackside.

I don't thing the bomb argument is too convincing. I could make a similar bomb argument which, if it were valid, would refute Lorentz contraction. Suppose there is a sensor which measures the length of a meterstick and triggers a bomb if the meterstick is exactly one meter. Since all observers will agree about whether the bomb went off or not, that means that all observers will be able to agree on what the length of the meterstick is.

What is the flaw in the argument? It lies in what the bomb actually does. The sensor must be moving in some inertial reference frame, and will only measure the meter stick in that reference frame. Different observers will differ about the length of the meterstick, but everyone will agree on the value that the sensor will observe. For instance, if the sensor is moving with the meterstick, then all observers will agree on the proper length of the meterstick. In the same way, the sensor in your bomb argument will be in a particular inertial reference frame, and so will only answer the question of whether the two events happen at the same time relative to that reference frame.

I'm not saying that you're wrong on your actual statement that all observers will agree on the simultaneity of events happening at the same place. I haven't studied relativity in sufficient detail to be absolutely sure one way or another. But I don't think the bomb argument is sufficient proof of your statement.

 

[Dale]

I'm not saying that you're wrong on your actual statement that all observers will agree on the simultaneity of events happening at the same place. I haven't studied relativity in sufficient detail to be absolutely sure one way or another. But I don't think the bomb argument is sufficient proof of your statement.

How about this one then:

By the Lorentz transform
$$dt'=\gamma(dt-v\,dx/c^2)$$
$$dx'=\gamma(dx-v\,dt)$$
so if dt=0 and dx=0 then dt'=0 and dx'=0 for any v.

 

[lugita15]

How about this one then:

By the Lorentz transform
$$dt'=\gamma(dt-v\,dx/c^2)$$
$$dx'=\gamma(dx-v\,dt)$$
so if dt=0 and dx=0 then dt'=0 and dx'=0 for any v.

OK, I'm convinced.

 

[yuiop]

How about this one then:

By the Lorentz transform
$$dt'=\gamma(dt-v\,dx/c^2)$$
$$dx'=\gamma(dx-v\,dt)$$
so if dt=0 and dx=0 then dt'=0 and dx'=0 for any v.

Nice succinct argument Dale.

 

[Aaron_Shaw]

I don't thing the bomb argument is too convincing. I could make a similar bomb argument which, if it were valid, would refute Lorentz contraction. Suppose there is a sensor which measures the length of a meterstick and triggers a bomb if the meterstick is exactly one meter. Since all observers will agree about whether the bomb went off or not, that means that all observers will be able to agree on what the length of the meterstick is.

What is the flaw in the argument? It lies in what the bomb actually does. The sensor must be moving in some inertial reference frame, and will only measure the meter stick in that reference frame. Different observers will differ about the length of the meterstick, but everyone will agree on the value that the sensor will observe. For instance, if the sensor is moving with the meterstick, then all observers will agree on the proper length of the meterstick. In the same way, the sensor in your bomb argument will be in a particular inertial reference frame, and so will only answer the question of whether the two events happen at the same time relative to that reference frame.

I'm not saying that you're wrong on your actual statement that all observers will agree on the simultaneity of events happening at the same place. I haven't studied relativity in sufficient detail to be absolutely sure one way or another. But I don't think the bomb argument is sufficient proof of your statement.

The sensore would always measure the meter stick, by definition, to be 1 meter in length.

 

[lugita15]

The sensor would always measure the meter stick, by definition, to be 1 meter in length.

When I say meter stick, I mean a stick with a proper length of one meter. But I think you knew that already.