Paradox within the twin paradox

[ghwellsjr]

Both counters measure exactly the same signal rate coming from the other counter, in this case 200 signals per minute. And from that, they each deduce that the other one's clock is running at 1% of their own clock rate.

You stated in your experiment:

If both counters view the other as going slow (ie. the light pulses, which represent the speed of time in the alternate reference frame from each reference frame are arriving with greater interval than the counters' own counter ticks), than this WOULD be impossible to reconcile;

So let's see what would happen if there were not the reciprocal time dilation. The traveling counter would send out 100 times more signals and the signal rate that the stationary counter would measure would be 20,000 signals per minute for a total of about 525600. And the traveling counter would receive the same number of signals but at 2 per minute. This is not reciprocal.

So hopefully, you still agree, and if that's that case, has the paradox gone away for you?

 

[teachmemore]

Let me be clear. I'm not trying to say that there is actually any paradox. I'm just trying to say that when the data transmission between the two counters is analysed under the laws of special relativity, the counters don't appear to "perceive" one another as running slower than themselves and yet, this does not seem to defy special relativity in any way.

 

[John232]

Since when from the Big Bang have two objects always traveled at a constant speed relative to each other?

 

[teachmemore]

Both counters measure exactly the same signal rate coming from the other counter, in this case 200 signals per minute. And from that, they each deduce that the other one's clock is running at 1% of their own clock rate.

You stated in your experiment:So let's see what would happen if there were not the reciprocal time dilation. The traveling counter would send out 100 times more signals and the signal rate that the stationary counter would measure would be 20,000 signals per minute for a total of about 525600. And the traveling counter would receive the same number of signals but at 2 per minute. This is not reciprocal.

So hopefully, you still agree, and if that's that case, has the paradox gone away?

OK. Maybe you have found where there is confusion. To me, the signal rate is what the clock uses to determine how fast the other clock is counting. So the clocks appear to perceive one another as counting faster than themselves, not slower.

 

[ghwellsjr]

Opps, we have simultaneity of posting (#36 and #37)

 

[teachmemore]

Opps, we have simultaneity of posting (#36 and #37)

That is impossible! I'm in a different reference frame (spaceship).

 

[pervect]

I agree this was ill-defined. I understand the relativity of simultaneity and should clarify this thought experiment by defining this simultaneity with the description I provided in post #30. I expected someone might make the objection you made here.

A special switching device in the stationary reference frame, but in a different location in space would be triggered by a passing counter, which would simultaneously reset its counter. The device would simultaneously send a light pulse to the stationary counter. The stationary counter, by knowledge of the distance between the device and itself would then set its counter to 0 and add the amount of time to its counter required to send the light signal to it from the device.

Which distance do you mean? The distance in the stationary frame? "The distance" will in general depend on the frame.

 

[teachmemore]

Which distance do you mean? The distance in the stationary frame? "The distance" will in general depend on the frame.

That is correct. The distance between the device and the counter in the stationary frame as measured from the stationary frame. Both the device and one counter are in the same frame, but at a great distance apart.

 

[ghwellsjr]

OK. Maybe you have found where there is confusion. To me, the signal rate is what the clock uses to determine how fast the other clock is counting. So the clocks appear to perceive one another as counting faster than themselves, not slower.

No, the rate at which the signals arrive is not the same as the rate they are sent out and this is caused by the relative motion. The point is that when both counters/clocks/observers are sending out pulses/signals/ticks at what they perceive to be the same rate as defined by their own clocks, then the rate at which they are received by the other one, taking into account the light travel time, their relative motion, and as measured by their own clock, results in them both measuring an identical signal rate coming from the other one.

In your scenario, you had the traveling counter approaching the stationary one which made the signal rate go up. But consider what happens when the traveler goes past the stationary one. Now the signal rate will go down from 200 per minute to 1 every 200 minutes but it still calculates to the same reciprocal time dilation factor.

 

[teachmemore]

No, the rate at which the signals arrive is not the same as the rate they are sent out and this is caused by the relative motion. The point is that when both counters/clocks/observers are sending out pulses/signals/ticks at what they perceive to be the same rate as defined by their own clocks, then the rate at which they are received by the other one, taking into account the light travel time, their relative motion, and as measured by their own clock, results in them both measuring an identical signal rate coming from the other one.

In your scenario, you had the traveling counter approaching the stationary one which made the signal rate go up. But consider what happens when the traveler goes past the stationary one. Now the signal rate will go down from 200 per minute to 1 every 200 minutes but it still calculates to the same reciprocal time dilation factor.

I did not say that the rate at which they arrived is the same as the rate at which they are sent out. I don't know where you got that from. In fact, I said the exact opposite. Yes what you say is obvious to me.

Also I need to correct something in this thought experiment that arises from my post #30 there. The stationary counter could not possibly send out its first pulse when the device is triggered.

So the thought experiment needs to be revised. When the stationary counter receives its first pulse, it calculates the elapsed time in its reference frame based on the distance from the triggered device and begins to send pulses back to the moving counter.

We can clarify this experiment in the following way:

These counters simply count at an even time interval in their own reference frame, and they also count incoming light pulses.

Once the stationary counter has done its calculation and set its counter, it sends out a number of pulses equivalent to the its starting count, and then continues to count at a 1 minute interval.

When the moving counter approaches the stationary counter, it has counted fewer times than the number of pulses it has received and the stationary counter has counted greater times than the number of pulses it received.

The question then becomes this:

If the two counters are equally relative to one another, how did one counter send more pulses than the other? Both the number of pulses and the number of counts should be equal.

I don't believe that this defies special relativity. I think there is a difference between what can be perceived by data transmission and what special relativity says about relative motion and time.

 

[John232]

In the light clock thought experiment there is no uncertainty of the speed and position of the photon. I would think that the number of counts should be equal also if the position was simultanous for the photon for each observer, but they are not certain of the exact position. They seem to know a lot about the speed of the photon too...

 

[JesseM]

Also I need to correct something in this thought experiment that arises from my post #30 there. The stationary counter could not possibly send out its first pulse when the device is triggered.

Instead of having a scheme with a "switching device" sending a signal to get both counters started, you could just have both counters programmed to calculate the current time in the stationary frame, and then have them both start sending signals at a pre-decided time-coordinate in the stationary frame.

The question then becomes this:

If the two counters are equally relative to one another, how did one counter send more pulses than the other? Both the number of pulses and the number of counts should be equal.

I don't believe that this defies special relativity. I think there is a difference between what can be perceived by data transmission and what special relativity says about relative motion and time.

Each counter sees the same ratio between (rate other counter's signals are arriving)/(rate I am sending signals). In this case, since the counters are moving towards each other each sees the other's signals coming in faster than they themselves are sending signals. However, if they each start sending signals simultaneously in the stationary frame (as would be true under my assumption above), then their view of one another is not completely symmetrical, because the delay that each counter sees between the time it started sending signals and the time it sees the first signal from the other counter will not be equal due to the relativity of simultaneity, so the stationary counter sees a greater delay and thus receives less signals in total from the moving counter than the moving counter receives from the stationary counter.

For example, suppose in the stationary frame the stationary counter is at x=0 light-years, and the moving counter is moving towards it at 0.6c, and at t=0 years the moving counter is at x=30 light-years, and both counters start sending signals at t=0, each sending signals at a rate of 1 per year according to their own clock. Then the two counters will meet after a time of 30/0.6 = 50 years in this frame. Since the moving counter sends the first signal at t=0 from 30 light-years away, the stationary counter receives the first signal at t=30, a delay of 30 years. Meanwhile, at t=18.75 years, the moving counter will be at position x=30 - 0.6*18.75 = 18.75 light-years, and naturally the first signal from the stationary counter will also be at x=18.75 light-years at time t=18.75 years, so that's when the moving counter receives the first signal. And in fact the delay is even smaller according to the moving counter's clock, since in the stationary frame it's running slow by $$\sqrt{1 - 0.6^2} = 0.8$$, so the moving counter only experiences a delay of 0.8*18.75 = 15 years between sending its own first signal and receiving the first signal from the stationary counter.

After each starts receiving signals from the other, they will each receive them at a rate of 2 per year according to their own clock, since the relativistic Doppler effect equation says $$f_{received} = f_{sent} \sqrt{\frac{1 + v/c}{1 - v/c}}$$, so with v/c = 0.6 the received frequency is greater than the sent frequency by a factor of $$\sqrt{\frac{1.6}{0.4}} = \sqrt{4} = 2$$. So if the stationary counter receives the first signal when its own clock reads 30 years, and meets the moving counter when its own clock reads 50 years, it must have received 40 signals from the moving counter in this time. Meanwhile if the moving counter receives its first signal at t=18.75 years and meets the stationary counter at t=50 years, a time-interval of 31.25 years in the stationary frame, according to its own clock the time between receiving the first signal and meeting the stationary counter must be 0.8*31.25 = 25 years, so it has received a total of 50 signals from the stationary counter.

 

[John232]

In the light clock thought experiment there is no uncertainty of the speed and position of the photon. I would think that the number of counts should be equal also if the position was simultanous for the photon for each observer, but they are not certain of the exact position. They seem to know a lot about the speed of the photon too...

Both observers would agree on the number of ticks of a certain clock but their own separate clocks would tick by different amounts since the other clock would be seen to use a longer distance of travel for the photon because of its motion while their own clock would use a shorter distance so then they would see each others time slow down relative to themselves.

 

[JesseM]

I am confused about the "moving clocks" part. For twin A on Earth, twin B is traveling is at a velocity +v. For the twin B who is traveling, twin A on Earth is moving at a velocity -v. And i thought that Special Relativity refers that no inertial frame is special; meaning twin B moving nearly at the speed of light should not be special.

Yes, no inertial frame is special. But if B turns around to return to Earth, then B has changed velocities relative to every inertial frame, there is no inertial frame that says that it's A that changed velocities rather than B. So, the situation is not symmetrical. And every inertial frame agrees that a constant-velocity path between two points elapses more time than a path with varying velocity, this is analogous to the way a straight line between two points on a 2D plane always has a shorter length than a path with varying slope (I expand on this geometrical analogy in [post=2972720]this post[/post]).

The only part that i see is different is that twin B requires acceleration +a to go somewhere and then an acceleration -a with respect to twin A to come back. Then if acceleration is the cause, how come Lorentz factor in time dilation does not include acceleration?

Again you may find it helpful to read the geometrical analogy in the post above. In terms of the analogy, the idea that time dilation depends only on velocity is analogous to the fact that a particular quantity on a 2D plane--namely, the rate that a car's odometer is increasing relative to increase in x-coordinate--can be expressed solely as a function of the slope S of the path the car is driving on (with S analogous to velocity) and not the rate the slope is changing dS/dx (analogous to acceleration), with the odometer increasing by an amount $$\Delta x \sqrt{1 + S^2}$$ for each increase in x-coordinate $$\Delta x$$ (analogous to the fact that the time dilation equation says a moving clock's reading will increase by an amount $$\Delta t \sqrt{1 - v^2/c^2}$$ when the time-coordinate of the frame you're using increases by $$\Delta t$$). And yet it is still true that a constant-slope path between two points (a straight line) always has a shorter distance than a path with varying slope, analogous to the fact that a constant-velocity path between two events (like the twins departing from one another and reuniting) always has a greater elapsed time than a non-constant-velocity path between the same two events.

 

[Grep]

I recognize quality explaining when I see it, and this thread delivers.

 

[ghwellsjr]

I said:

Both counters measure exactly the same signal rate coming from the other counter, in this case 200 signals per minute.

Then you said:

OK. Maybe you have found where there is confusion. To me, the signal rate is what the clock uses to determine how fast the other clock is counting. So the clocks appear to perceive one another as counting faster than themselves, not slower.

And from that, I deduced that since I had just said that each counter measures the signal rate coming from the other counter at 200 signals per second (when they are each sending out 1 signal per minute), that you had concluded that they "appear to perceive one another as counting faster than themselves, not slower". And so I said:

No, the rate at which the signals arrive is not the same as the rate they are sent out and this is caused by the relative motion.

And then you said:

I did not say that the rate at which they arrived is the same as the rate at which they are sent out. I don't know where you got that from. In fact, I said the exact opposite. Yes what you say is obvious to me.

If it's obvious to you, then why did you say "appear to perceive one another as counting faster than themselves, not slower"? Do you understand that there is a reciprocal relationship between the rates at which two moving observers receive periodic signals from the other one when they are both emitting at the same rate and that this can only happen if they each perceive the other's clock as running slow? And do you understand that the reason why the rate is much higher than might be obvious is because the traveling counter is going toward the stationary counter and as soon as it passes the stationary counter, the rate suddenly drops from 200 signals per minute to 0.005 signals per minute (or one signal every 200 minutes) because they are now getting farther apart, but the same reciprocal time dilation applies? I'm only asking because these things are not obvious to me.

Also I need to correct something in this thought experiment that arises from my post #30 there. The stationary counter could not possibly send out its first pulse when the device is triggered.

So the thought experiment needs to be revised. When the stationary counter receives its first pulse, it calculates the elapsed time in its reference frame based on the distance from the triggered device and begins to send pulses back to the moving counter.

We can clarify this experiment in the following way:

These counters simply count at an even time interval in their own reference frame, and they also count incoming light pulses.

Once the stationary counter has done its calculation and set its counter, it sends out a number of pulses equivalent to the its starting count, and then continues to count at a 1 minute interval.

When the moving counter approaches the stationary counter, it has counted fewer times than the number of pulses it has received and the stationary counter has counted greater times than the number of pulses it received.

I wish you hadn't brought this up. I really don't understand what the problem is that you are trying to fix here. Look at my interpretation in post #31 of your scenario. Since you are defining what is happening in a particular reference frame, it is perfectly legitimate for you to say that both counters start at the same exact time. So let's go back to that scenario and don't worry about how the counters knew when to start counting and simultaneously start emitting their signals.

OK
The question then becomes this:

If the two counters are equally relative to one another, how did one counter send more pulses than the other? Both the number of pulses and the number of counts should be equal.
.

I thought I explained this in post #31 but let me reiterate. The traveling counter is counting at a slower rate than the stationary counter. In fact, it is counting at 1% so it only emits 1/100 of the number of signals and its counter is 1/100 of the stationary counter at the time when they meet. So the traveling counter emitted 5256 signals and the stationary counter counted 5256 signals and when they met, the traveling counter communicated to the stationary counter that it was on count 5256 which matched what the stationary counter counted. And during the same one-year interval of time, the stationary counter emitted 525600 signals and the traveling counter counted all 525600 signals and when they met, the stationary counter communicated to the traveling counter that it was on count 525600 which matched what the traveling counter counted.

Now, maybe you are asking why there are two different counter numbers involved here and that's because, as far as the traveling counter is concerned, the whole scenario took place in 3.65 days whereas for the stationary counter, it took a whole year. But they both are emitting at the same rate of 1 signal per minute (according to their own timebase) and they are both detecting (once the detection starts) at 200 signals per minute (again, according to their own timebase), which, based on the relative velocity and knowing the rate of signal emission, they can each calculate the other one to have a slow timebase of 1% of their own.

OK
I don't believe that this defies special relativity. I think there is a difference between what can be perceived by data transmission and what special relativity says about relative motion and time.

Of course it doesn't defy SR but I don't know what you mean in the next sentence--no idea at all.

So now are all the issues cleared up or do you still have unresolved questions?

 

[teachmemore]

I said:

Then you said:

And from that, I deduced that since I had just said that each counter measures the signal rate coming from the other counter at 200 signals per second (when they are each sending out 1 signal per minute), that you had concluded that they "appear to perceive one another as counting faster than themselves, not slower". And so I said:

And then you said:

If it's obvious to you, then why did you say "appear to perceive one another as counting faster than themselves, not slower"? Do you understand that there is a reciprocal relationship between the rates at which two moving observers receive periodic signals from the other one when they are both emitting at the same rate and that this can only happen if they each perceive the other's clock as running slow? And do you understand that the reason why the rate is much higher than might be obvious is because the traveling counter is going toward the stationary counter and as soon as it passes the stationary counter, the rate suddenly drops from 200 signals per minute to 0.005 signals per minute (or one signal every 200 minutes) because they are now getting farther apart, but the same reciprocal time dilation applies? I'm only asking because these things are not obvious to me.

I wish you hadn't brought this up. I really don't understand what the problem is that you are trying to fix here. Look at my interpretation in post #31 of your scenario. Since you are defining what is happening in a particular reference frame, it is perfectly legitimate for you to say that both counters start at the same exact time. So let's go back to that scenario and don't worry about how the counters knew when to start counting and simultaneously start emitting their signals.

I thought I explained this in post #31 but let me reiterate. The traveling counter is counting at a slower rate than the stationary counter. In fact, it is counting at 1% so it only emits 1/100 of the number of signals and its counter is 1/100 of the stationary counter at the time when they meet. So the traveling counter emitted 5256 signals and the stationary counter counted 5256 signals and when they met, the traveling counter communicated to the stationary counter that it was on count 5256 which matched what the stationary counter counted. And during the same one-year interval of time, the stationary counter emitted 525600 signals and the traveling counter counted all 525600 signals and when they met, the stationary counter communicated to the traveling counter that it was on count 525600 which matched what the traveling counter counted.

Now, maybe you are asking why there are two different counter numbers involved here and that's because, as far as the traveling counter is concerned, the whole scenario took place in 3.65 days whereas for the stationary counter, it took a whole year. But they both are emitting at the same rate of 1 signal per minute (according to their own timebase) and they are both detecting (once the detection starts) at 200 signals per minute (again, according to their own timebase), which, based on the relative velocity and knowing the rate of signal emission, they can each calculate the other one to have a slow timebase of 1% of their own.

Of course it doesn't defy SR but I don't know what you mean in the next sentence--no idea at all.

So now are all the issues cleared up or do you still have unresolved questions?

All agreed.

But, the issue is that the traveling counter has seen 525600 signals over a duration of 3.65 days. While the stationary counter has seen 5256 signals over the duration of a year. Which means that the stationary counter sees the traveling counter as running slower than itself, while the traveling counter sees the stationary counter as running faster than itself. You don't see a problem with this? I think most would say that both counters should see the other one as running slow. But that doesn't appear to be the case.

These signals are what the counters use to measure the rate of time in the alternate reference frame. Since both counters are approaching one another, should they not both see the other counter as counting slower than themselves? If the motion of these reference frames is only "relative", than why should time in one reference frame move slower than time in the other?

What I'm trying to say is that the fact that one counter is moving faster than the other is significant to this problem. That these two counters are moving relative to one another is not enough information, we also need to know that one is moving near c, and the other is not.

Does this make sense?

The light signals are like the ticking of a clock. These light signals are what are used to perceive the rate of time in the alternate reference frame.

 

[JesseM]

All agreed.

But, the issue is that the traveling counter has seen 525600 signals over a duration of 3.65 days. While the stationary counter has seen 5256 signals over the duration of a year. Which means that the stationary counter sees the traveling counter as running slower than itself, while the traveling counter sees the stationary counter as running faster than itself. You don't see a problem with this? I think most would say that both counters should see the other one as running slow. But that doesn't appear to be the case.

It will be the case if you look at the rate that each is seeing signals during a period when they were actually receiving signals the whole time, not the total number of signals each received during a period which might include a lot of "dead air" because it was before they had received the first signal from the other one. In this example the gamma-factor is 100, so the relative velocity must be 0.999949998749938c, which means the relativistic Doppler shift is sqrt[(1 + 0.999949998749938)/(1 - 0.999949998749938)] = 199.994999875905, so if each is sending signals at 1 per minute, then during any period when they are receiving signals from the other, they will be receiving them at a rate of about 199.995 per minute.

What I'm trying to say is that the fact that one counter is moving faster than the other is significant to this problem. That these two counters are moving relative to one another is not enough information, we also need to know that one is moving near c, and the other is not.

Does this make sense?

Definitely not, there is no objective truth about which is "moving near c" and which is "stationary", that depends on your frame of reference. Whatever is happening with the counters in the "stationary" frame, you could construct an analogous pair where the choice of when each counter started sending signals was different, in such a way that the counter which was "travelling" relative to the stationary frame would be the one to receive 5265 signals over the course of a year of its own proper time (would actually be 100 years in the stationary frame), while the counter that was at rest in the stationary frame would receive 525600 over 3.65 days in the stationary frame, and yet each counter started sending signals simultaneously in the rest frame of the traveling counter (not simultaneously in the stationary frame).

 

[teachmemore]

No, the rate at which the signals arrive is not the same as the rate they are sent out and this is caused by the relative motion. The point is that when both counters/clocks/observers are sending out pulses/signals/ticks at what they perceive to be the same rate as defined by their own clocks, then the rate at which they are received by the other one, taking into account the light travel time, their relative motion, and as measured by their own clock, results in them both measuring an identical signal rate coming from the other one.

In your scenario, you had the traveling counter approaching the stationary one which made the signal rate go up. But consider what happens when the traveler goes past the stationary one. Now the signal rate will go down from 200 per minute to 1 every 200 minutes but it still calculates to the same reciprocal time dilation factor.

Oh geeze. I am so sorry. I do apologize. What you said here was clearly not obvious to me, because it was exactly what I've been trying to put my finger on, and it is exactly what I meant when I made that confusing statement about data transmission being different than relative motion/time dilation.

Ya. My whole point by all this is that what somebody visualizes from their frame of reference doesn't necessarily correspond with the time dilation factors.

The light pulses reaching the counters are what is visualized; which is different than the relative time of these two reference frames. Which is the same for both. And each alternate reference frame is slower for both; even though what they visualize is very different.

 

[JesseM]

Oh geeze. I am so sorry. I do apologize. What you said here was clearly not obvious to me, because it was exactly what I've been trying to put my finger on, and it is exactly what I meant when I made that confusing statement about data transmission being different than relative motion/time dilation.

Ya. My whole point by all this is that what somebody visualizes from their frame of reference doesn't necessarily correspond with the time dilation factors.

The light pulses reaching the counters are what is visualized; which is different than the relative time of these two reference frames. Which is the same for both. And each alternate reference frame is slower for both; even though what they visualize is very different.

By "what they visualize" do you mean how fast they see the signals coming in? Like I said, that's given by the relativistic Doppler shift equation, and for two observers moving at constant relative velocity the visual rates are completely symmetrical (if counter #1 sees signals from counter #2 coming in at about 200 per minute, then counter #2 must also see signals from counter #1 coming in at about 200 per minute).

 

[ghwellsjr]

It's all explained, right here in post #31:

...
Just think about something. When this scenario starts, neither counter will have any knowledge of what the other counter is doing. It will take almost one year for the signals coming from the traveling counter to reach the stationary counter and then within less than half an hour, all the signals will arrive in a burst and then the counter will arrive. At a speed of 0.99995c, the traveling counter's time has slowed to 1% of normal. Since there are 525600 minutes in a year, this counter will have only sent out 5256 signals during his entire trip but they will arrive during the last 26.28 minutes (1-0.99995 or 0.00005 times the number of minutes in a year). That's a rate of 200 signals per minute as measured by the stationary clock.

On the other hand, the traveling counter will not see anything from the stationary counter until after about half a year. Then it will start seeing signals coming in two per minute (they are traveling towards him at the speed of light and he is traveling toward them at almost the speed of light, which approximately doubles the rate at which he receives the signals), except since his clock is running at 1% of normal, he will think they are coming in at 100 times that rate which is 200 per minute. And by the time he gets to the stationary clock, he will have received almost a year's worth of signals sent out at one per minute or very nearly 525600.

 

[teachmemore]

By "what they visualize" do you mean how fast they see the signals coming in? Like I said, that's given by the relativistic Doppler shift equation, and for two observers moving at constant relative velocity the visual rates are completely symmetrical (if counter #1 sees signals from counter #2 coming in at about 200 per minute, then counter #2 must also see signals from counter #1 coming in at about 200 per minute).

How is this symmetrical if there is an unequal number of pulses exchanged between these counters? At any time near the end of the voyage, the traveling counter can determine that he is moving faster than the stationary one by comparing the total pulses received with the total counts made.

 

[teachmemore]

It will be the case if you look at the rate that each is seeing signals during a period when they were actually receiving signals the whole time, not the total number of signals each received during a period which might include a lot of "dead air" because it was before they had received the first signal from the other one. In this example the gamma-factor is 100, so the relative velocity must be 0.999949998749938c, which means the relativistic Doppler shift is sqrt[(1 + 0.999949998749938)/(1 - 0.999949998749938)] = 199.994999875905, so if each is sending signals at 1 per minute, then during any period when they are receiving signals from the other, they will be receiving them at a rate of about 199.995 per minute.

Definitely not, there is no objective truth about which is "moving near c" and which is "stationary", that depends on your frame of reference. Whatever is happening with the counters in the "stationary" frame, you could construct an analogous pair where the choice of when each counter started sending signals was different, in such a way that the counter which was "travelling" relative to the stationary frame would be the one to receive 5265 signals over the course of a year of its own proper time (would actually be 100 years in the stationary frame), while the counter that was at rest in the stationary frame would receive 525600 over 3.65 days in the stationary frame, and yet each counter started sending signals simultaneously in the rest frame of the traveling counter (not simultaneously in the stationary frame).

This here is what I need to think about.

I was under the impression that the traveling counter counts more slowly simply because it is travelling, and so, knowledge about which one is traveling is crucial to determining which counter counts the fewest times.

 

[JesseM]

How is this symmetrical if there is an unequal number of pulses exchanged between these counters? At any time near the end of the voyage, the traveling counter can determine that he is moving faster than the stationary one by comparing the total pulses received with the total counts made.

Again, the rate that they each see signals arriving from the other counter is symmetrical. But if you impose the rule that they both start sending signals at the same time in the stationary frame, then the stationary counter won't see signals start to arrive (beginning with the first one sent by the traveling counter) until shortly before they meet, while the traveling counter will see signals start to arrive long before meeting the stationary counter. But this asymmetry has nothing to do with the basic laws of physics, it's just a consequence of the rule that both started sending signals simultaneously in the stationary frame; if you instead imposed the rule that both started sending signals simultaneously in the traveller's rest frame, then the reverse would be true, with the stationary counter seeing signals start to arrive long before they meet and the traveling counter not seeing signals start to arrive until shortly before they meet.

 

[JesseM]

This here is what I need to think about.

I was under the impression that the traveling counter counts more slowly simply because it is travelling

By "counts more slowly" do you just mean how fast its own clock is ticking, or are you talking about the rate it receives signals from the other counter? If you're just talking about clock rates (the rate it counts seconds), then relative to the "stationary" frame its clock does tick more slowly, but not in any absolute sense. In the traveling counter's own rest frame, its clock is ticking normally while the stationary counter's clock is ticking slowly.

and so, knowledge about which one is traveling is crucial to determining which counter counts the fewest times.

It's crucial to understand that in relativity all inertial frames are equally valid as far as the basic laws of physics are concerned (the http://nobelprize.org/educational/physics/relativity/postulates-1.html), there is no frame-independent objective truth about who is "really" moving at a greater velocity, for any pair of objects in relative motion you can choose either object's inertial rest frame to analyze the situation, and the laws of physics will work the same way in this frame as any other frame (including the law that says a clock moving at velocity v relative to the frame is running slow by $$\sqrt{1 - v^2/c^2}$$ relative to the time coordinate of that frame).

 

[ghwellsjr]

How is this symmetrical if there is an unequal number of pulses exchanged between these counters? At any time near the end of the voyage, the traveling counter can determine that he is moving faster than the stationary one by comparing the total pulses received with the total counts made.

This here is what I need to think about.

I was under the impression that the traveling counter counts more slowly simply because it is travelling, and so, knowledge about which one is traveling is crucial to determining which counter counts the fewest times.

Maybe you could benefit from my explanation of relativistic doppler in this post (#4) on another thread:
https://www.physicsforums.com/showpost.php?p=2970458&postcount=4

There are two important things to recognize here. First, it is the relativistic doppler that is the means by which each observer recognizes that the other one's clocks are running slower than their own. But it is not just the rate that each receives the signals that is necessary for them to make this determination, they also need to know (by prior agreement) that each one is emitting the signals at what they each consider to be the same rate, and they need to know the relative speed, either by prior agreement or knowledge (as is the case when twins start out together and one "tells" the other one what speed he will be traveling at) or by measuring the speed of the other one and this they can do by sending a series of signal to the other one which is reflected back to them. Of course all this takes time and is somewhat complicated to explain. All we are doing here is illustrating for us (because we have more knowledge than the observers/counters/clocks in the scenario) how the relativistic doppler works.

And the second thing to recognize is that if it weren't for the reason that we need SR, the doppler would not be symmetric and it would be dependent on the relative speed of the other body and the speed of each body in the medium, in this case the absolute at-rest aether.

 

[teachmemore]

By "counts more slowly" do you just mean how fast its own clock is ticking, or are you talking about the rate it receives signals from the other counter? If you're just talking about clock rates (the rate it counts seconds), then relative to the "stationary" frame its clock does tick more slowly, but not in any absolute sense. In the traveling counter's own rest frame, its clock is ticking normally while the stationary counter's clock is ticking slowly.

I understand that in relativity all inertial frames are equally valid as far as the basic laws of physics are concerned. You are neglecting the fact that not all factors required to solve this problem lay within the confines of special relativity.

Specifically, special relativity does not say anything about deriving information about the present based on data preserved from the past; which is a crucial factor in understanding the thought experiment I have presented.

By insisting on understanding what happens for only the factors in this experiment for which special relativity applies, you have come to incorrect reasoning - specifically, about what is real or absolute, as defined by the experiment.

When I laid out this thought experiment, I explicitly stated that one counter is travelling, while the other is not. For you to think that special relativity tells you that you can not know which frame is moving faster is clearly false. Special relativity only tells you that you can not know which frame is moving faster by the factors of the scenario for which special relativity applies. It is easy to determine from one frame, that another frame is moving faster than it simply by looking at historically preserved information within that one frame.

Furthermore, although due to the laws of special relativity, we can never truly know which frame in the universe is the true stationary frame (at least I can't comprehend a way in which we would determine this). We can conceive a stationary frame, and it does not go against any known laws of physics for such a frame to exist - an absolute stationary frame. Again, special relativity does not say that such a frame does not exists, only that without prior knowledge, you can not determine whether you are in it.

But, for this thought experiment, I have clearly stated that one frame is stationary and the other frame is travelling. You cannot change these factors in the problem any more than you could do such a thing in reality. This does not defy special relativity. Such information is outside the confines of special relativity, because it is derived from properties of the universe for which special relativity says nothing about.

Again, special relativity only says something about what you can know through relativistic transformations. It does not tell you anything about what you can know through other means! It does not tell you about any absolute aspects of reality. It only tells you about relative qualities of reality.

I have clearly defined in my thought experiment that one counter is stationary and the other counter is travelling. It is perfectly reasonable to make such absolute statements, and these statements are made outside the confines of special relativity. These factors of the thought experiment cannot be changed.

Yes, again, I understand that this distinction does not make any difference to the physical laws experienced in each reference frame. Those laws are preserved by special relativity. But it does certainly make a difference to the absolute statements we can make about this hypothetical scenario. The moving counter does count fewer times than the stationary counter. That is an absolute which can not be changed. It is made absolute, because the fact that the stationary counter is stationary is also absolute, as well as the fact that the traveling counter is travelling, is not stationary, and is going at an absolute speed relative to c.

hmmm. All this makes me consider, the only absolute speeds in the universe have to be defined as a factor of c. Otherwise, the speed is relative. Anyway, does any of this make sense to you?

 

[teachmemore]

By "counts more slowly" do you just mean how fast its own clock is ticking, or are you talking about the rate it receives signals from the other counter? If you're just talking about clock rates (the rate it counts seconds), then relative to the "stationary" frame its clock does tick more slowly, but not in any absolute sense. In the traveling counter's own rest frame, its clock is ticking normally while the stationary counter's clock is ticking slowly.

Ok. Before you can help me to come to an understanding on this, we need to be on the same page.

I want to know if you agree with the following statement:

I have an "absolutely" stationary counter and I have an "absolutely" traveling counter. According to special relativity, the traveling counter "sees" only a moving counter and the stationary counter "sees" only a moving counter. Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past). In this case, both counters are moving slower relative to the other counter, but only one is "actually" moving slower - and that is the traveling counter.

Do you agree?

 

[JesseM]

I understand that in relativity all inertial frames are equally valid as far as the basic laws of physics are concerned. You are neglecting the fact that not all factors required to solve this problem lay within the confines of special relativity.

I don't see why they wouldn't...

Specifically, special relativity does not say anything about deriving information about the present based on data preserved from the past;

Not sure what you mean. Certainly in SR if you know the positions of various parts of a system at some point in the past you can use the dynamical equations of the laws of physics to predict how they will move around at later times, that's what all dynamical equations are designed to do. What specific "data preserved from the past" are you talking about in your example, and what "information about the present" is that data being used to derive?

By insisting on understanding what happens for only the factors in this experiment for which special relativity applies, you have come to incorrect reasoning - specifically, about what is real or absolute, as defined by the experiment.

Again more specifics would be helpful, what precisely do you think is "real or absolute", and not frame-dependent, in your experiment?

When I laid out this thought experiment, I explicitly stated that one counter is travelling, while the other is not.

I understood this to mean that one is traveling relative to the inertial frame we are using, not in any absolute sense. If you are saying that one counter is traveling in an absolute, frame-independent sense, then your scenario involves metaphysical claims that can't be verified experimentally, because there's no actual experimental way to test whether something is "travelling" in any frame-independent sense (no matter what experiment you think up, all frames will make the same predictions about the readings of your instruments, in spite of the fact that they have different opinions on whether any given instrument is 'travelling' or 'at rest')

For you to think that special relativity tells you that you can not know which frame is moving faster is clearly false.

The only notion of "motion" in relativity is relative motion, you can't talk about whether something is moving or at rest (or which of two objects is moving faster) in any absolute sense.

It is easy to determine from one frame, that another frame is moving faster than it simply by looking at historically preserved information within that one frame.

What do you mean "from one frame"? Of course I agree that relative to a specific choice of frame you can define the speed of any other frame or object, but I thought you were talking about deciding which is stationary and which is moving in a "real or absolute" sense. When you said it is "clearly false" that "you can not know which frame is moving faster", did you just mean "moving faster" in a relative, non-absolute sense? If so I don't know why you think I would deny that you can determine which of two objects or frames is moving faster relative to some specific frame, of course I would agree with that!

Furthermore, although due to the laws of special relativity, we can never truly know which frame in the universe is the true stationary frame (at least I can't comprehend a way in which we would determine this). We can conceive a stationary frame, and it does not go against any known laws of physics for such a frame to exist - an absolute stationary frame. Again, special relativity does not say that such a frame does not exists, only that without prior knowledge, you can not determine whether you are in it.

Well, belief in such an absolute stationary frame is a metaphysical hypothesis, like believing in God or the soul. Not only does relativity say that there is no empirical way to determine which frame is the absolute frame, it also says there is no physical reason why you need the hypothesis of an "absolute frame". Of course it also does not rule this hypothesis out, I actually made this point myself recently on [post=2980648]another thread[/post]:

Also note that you are free to believe that one inertial frame's definition of simultaneity is "correct" in some absolute metaphysical sense, as long as there is no physical experiment that will actually distinguish the "correct" inertial frame from any other inertial frame this does not conflict with SR, which is just meant to be a physical theory and not a metaphysical one.

But, for this thought experiment, I have clearly stated that one frame is stationary and the other frame is travelling.

You didn't state that one was "stationary" in an absolute metaphysical sense, I thought you just meant that we could adopt the terminology of calling one the "stationary" frame and one the "travelling" frame.

You cannot change these factors in the problem any more than you could do such a thing in reality.

Well, I didn't change that factor, I didn't say anything about any frame being stationary or at rest in an absolute sense. I just pointed out that, without changing the motion of the two counters, you could change when they were programmed to start transmitting signals (so they no longer started sending signals simultaneously in the stationary frame), and this would change the final number of signals each had received when they met.

Again, special relativity only says something about what you can know through relativistic transformations. It does not tell you anything about what you can know through other means! It does not tell you about any absolute aspects of reality. It only tells you about relative qualities of reality.

Relativity certainly tells you about frame-independent facts, it wouldn't be much use as a physical theory if it didn't! For example, it can tell you how much proper time will elapse between two events on an object's worldline (like the event of a person leaving his twin and the event of his reuniting with him), the answer to questions about proper time doesn't depend on what frame you use to do your calculations.

I have clearly defined in my thought experiment that one counter is stationary and the other counter is travelling. It is perfectly reasonable to make such absolute statements, and these statements are made outside the confines of special relativity. These factors of the thought experiment cannot be changed.

OK, as I said you never made clear that you were talking about absolute metaphysical truths outside the domain of physics. But even with that understanding, I don't see why you would disagree with anything I've said so far, I don't think I said anything about changing the definition of which counter is "stationary" for example. What specific previous statement of mine do you disagree with?

Yes, again, I understand that this distinction does not make any difference to the physical laws experienced in each reference frame. Those laws are preserved by special relativity. But it does certainly make a difference to the absolute statements we can make about this hypothetical scenario. The moving counter does count fewer times than the stationary counter. That is an absolute which can not be changed. It is made absolute, because the fact that the stationary counter is stationary is also absolute, as well as the fact that the traveling counter is travelling, is not stationary, and is going at an absolute speed relative to c.

Yes, if you believe in absolute time and space this is true, although this is a metaphysical faith I don't share (by http://en.wikipedia.org/wiki/Occam's_razor]Occam's[/PLAIN] razor it seems simpler to dispense with the idea of absolute motion and absolute simultaneity, since these things provide no useful explanatory role and we can have a perfectly good ontology of spacetime without them)

hmmm. All this makes me consider, the only absolute speeds in the universe have to be defined as a factor of c. Otherwise, the speed is relative. Anyway, does any of this make sense to you?

Yes, I think the distinction between absolute (but unverifiable) truths and physically-verifiable truths helps clarify what you're saying. Of course, about that last part, if there is an absolute time and space then the speeds of slower-than-light objects are absolute too, although in physics terms they are relative.

 

[JesseM]

want to know if you agree with the following statement:

I have an "absolutely" stationary counter and I have an "absolutely" traveling counter. According to special relativity, the traveling counter "sees" only a moving counter and the stationary counter "sees" only a moving counter. Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past). In this case, both counters are moving slower relative to the other counter, but only one is "actually" moving slower - and that is the traveling counter.

Do you agree?

I agree that if there is such a thing as absolute time and space, then there will be some absolute truth about which is "really" moving at a smaller speed and which is "really" sending signals more quickly, but this truth would be impossible to determine by any empirical means, and personally I don't actually believe in absolute time and space, it seems like an unnecessarily cumbersome idea given that it would play no useful role in explaining anything (by analogy, do you believe in an 'absolute left and right'?) And I don't understand the statement "Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past)"--why would acceleration in the past tell you anything about which is moving in an absolute sense? You can always find an inertial frame where the two counters were initially traveling together at some nonzero speed, then the acceleration of one counter caused it to come to rest in that frame, and since the "absolute frame" is completely unknowable we have no reason to rule out the idea that this frame is in fact the absolute one.

 

[teachmemore]

Definitely not, there is no objective truth about which is "moving near c" and which is "stationary", that depends on your frame of reference. Whatever is happening with the counters in the "stationary" frame, you could construct an analogous pair where the choice of when each counter started sending signals was different, in such a way that the counter which was "travelling" relative to the stationary frame would be the one to receive 5265 signals over the course of a year of its own proper time (would actually be 100 years in the stationary frame), while the counter that was at rest in the stationary frame would receive 525600 over 3.65 days in the stationary frame, and yet each counter started sending signals simultaneously in the rest frame of the traveling counter (not simultaneously in the stationary frame).

You see. Your thinking is so focused on the relative aspects of this thought experiment that you fail to see the non-relative ones; which would allow you to come to an absolute answer about the pulses seen by each of these counters.

It appears to me that the added complexity you have introduced by neglecting the absolute states of this thought experiment is causing you to confuse what is possible in reality with what is possible when only special relativity is taken into account. ie. In your abstract example here what you have basically done is moved the stationary frame to the traveling frame - ie. symmetrically swapped frames - which is physically impossible. It could never be done in reality, because there is more to be taken into account than just special relativity. Other physical aspects of reality would be broken. You would basically be forced to brake the continuity of information through time.

There is definitely objective truth about which is moving and which is not. It is defined/ingrained in the very nature of the thought experiment just as a rocket, which had accelerated away from the Earth would be known by the people in the rocket and the people on Earth to be traveling faster than Earth relative to c and would be an absolute fact that is ingrained in the reality of the universe.

 

[teachmemore]

I agree that if there is such a thing as absolute time and space, then there will be some absolute truth about which is "really" moving at a smaller speed and which is "really" sending signals more quickly, but this truth would be impossible to determine by any empirical means, and personally I don't actually believe in absolute time and space, it seems like an unnecessarily cumbersome idea given that it would play no useful role in explaining anything (by analogy, do you believe in an 'absolute left and right'?) And I don't understand the statement "Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past)"--why would acceleration in the past tell you anything about which is moving in an absolute sense? You can always find an inertial frame where the two counters were initially traveling together at some nonzero speed, then the acceleration of one counter caused it to come to rest in that frame, and since the "absolute frame" is completely unknowable we have no reason to rule out the idea that this frame is in fact the absolute one.

Ah. Excellent! So this is where there is confusion between us.

To me, it sounds like your mind is totally stuck in the relative.

c is absolute. correct?

So if the Earth is moving at a factor of c, say X*c, if a rocket accelerates away from the Earth in any arbitrary direction, how could it possible be moving slower than X*c?

It sounds to me like you object to notating speed as a factor of c? Because if a speed of a factor of c were possible, it would imply that absolute speeds are in fact possible.

 

[teachmemore]

Let me pose this question to you then and see if you can answer it:

If I am moving slower than the speed of light, how is it possible that I am not moving at a fraction of the speed of light? And if I am moving at a fraction of the speed of light, then how is it possible that my speed is not absolute?

 

[teachmemore]

Yes, I think the distinction between absolute (but unverifiable) truths and physically-verifiable truths helps clarify what you're saying. Of course, about that last part, if there is an absolute time and space then the speeds of slower-than-light objects are absolute too, although in physics terms they are relative.

Not in "Physics" terms. In "Special Relativity" terms. Special Relativity only deals with the relative aspects of reality. Where as not all problems in physics deal with the purely relative; as I am trying to point out.

 

[JesseM]

You see. Your thinking is so focused on the relative aspects of this thought experiment that you fail to see the non-relative ones; which would allow you to come to an absolute answer about the pulses seen by each of these counters.

Huh? What am I failing to see? I already acknowledged you are free to introduce the idea of absolute time and space, I just pointed out that you hadn't explained clearly that this was what you were doing, and also that I don't personally believe in such an entity.

It appears to me that the added complexity you have introduced by neglecting the absolute states of this thought experiment is causing you to confuse what is possible in reality with what is possible when only special relativity is taken into account.

Can you be more specific about what you think I have said that is wrong or confused?

ie. In your abstract example here what you have basically done is moved the stationary frame to the traveling frame - ie. symmetrically swapped frames - which is physically impossible.

No I didn't, you are obviously misunderstanding something. All I suggested was that we can change the timing of when each counter starts sending signals, and this will change the fact about which counter has received more signals when they meet. This needn't change the fact about which counter is in a state of absolute rest and which is in a state of absolute motion, it just means that in absolute terms they sent their first signals non-simultaneously rather than simultaneously (though in relative terms, they did send their first signals simultaneously in the rest frame of the traveling counter, it's just that this frame's definition of simultaneity does not match with absolute simultaneity). Since human experiments will have no way of knowing which counter is "stationary" in absolute terms (even if we, in our godlike role as the ones who define the thought-experiment, do know that), they will have no way of knowing it is more "accurate" to program the counters to start sending signals simultaneously in the first counter's frame rather than in the second counter's frame.

There is definitely objective truth about which is moving and which is not.

That's a statement of metaphysical faith on your part, akin to saying "there is definitely a God" or "there is definitely an absolute truth about which counter is 'further to the left' in an absolute sense, not just relative to some observer". I am agnostic about God but very skeptical about the idea of "absolute left" or "absolute time", they seem like totally superfluous metaphysical ideas to me, much easier to just adopt an eternalist ontology where all points in spacetime are equally real and there is no need for any absolute truth about simultaneity.

It is defined/ingrained in the very nature of the thought experiment

If you want to do a thought experiment which assumes there is such a thing as absolute space and time I'm happy to go along with that for the purposes of discussion, even though I don't really believe in such notions. Again, nothing I said required changing the definition of which counter was "really" moving or which clock was "really" ticking slower.

just as a rocket, which had accelerated away from the Earth would be known by the people in the rocket and the people on Earth to be traveling faster than Earth relative to c

Huh? No it wouldn't, not even if absolute time and space existed. How can you rule out the idea that the Earth was already moving at some large speed, say 0.8c, relative to absolute space? You're not a geocentrist are you? If you agree there's no way any human could rule out such a possibility, then obviously if the rocket accelerated away from the Earth in the opposite direction from the direction the Earth is moving in an absolute sense, then as the rocket accelerates its absolute speed will decrease, not increase. (Perhaps the word 'acceleration' is confusing you, in physics the term simply refers to any change in speed whether an increase or a decrease, and even if there was such a thing as absolute speed, if relativity is correct acceleration at 1G should feel exactly the same regardless whether your absolute speed is increasing or decreasing. Didn't you agree earlier that even if absolute motion exists, there would be no experimental way to determine which frame is the absolute frame?)