Einstein Special on PBS
So, here's how I finally grokked this stuff. c, the speed of light in a vacuum, is often spoken of as a "speed limit" that nothing can ever exceed. That's a bad way to put it, and people who have expressed it that way in popular science writing for 100 years should feel bad.
Instead, the way to visualize relativity is to realize that c is the only speed at which anything can travel. You are always moving at 300,000,000 meters per second, whether you want to or not. But you're doing it through all four dimensions including time. If you choose to remain stationary in (x,y,z), then all of your velocity is in the t direction. If you move through space at 100,000,000 meters per second in space, then your velocity in the t direction is 283,000,000 meters per second (because sqrt(100E6^2 + 283E6^2) = 300E6.)
It doesn't make sense to speak of moving a certain number of "meters" through time, so your location in time itself is what has to change. You won't perceive any drift in your personal timebase when you move in space, any more than you will perceive a change in your location relative to yourself. ("No matter where you go, there you are.") But an independent observer will see a person who's moving at 100,000,000 meters per second in x,y,z and 283,000,000 meters per second in t. They see you moving in space, in the form of a location change, and they also see you moving in time, in the form of a disagreement between their perception of elapsed time and your own.
Likewise, if you spend all of your velocity allowance in (x,y,z), your t component is necessarily zero. Among other inconvenient effects that occur at dt/dt=0, you won't get any closer to your destination, even though your own watch is still ticking normally. Particles moving near c experience this effect from their point of view, even while we watch them smash into their targets at unimaginable speeds.
This is special relativity in action. The insight behind general relativity is twofold: 1) movement caused by the acceleration of gravity is indistinguishable from movement caused by anything else; and 2) you don't even have to move, just feel the acceleration. That second part was what really baked peoples' noodles. It is what's responsible for the disagreement between the two 5071As.
-- john, KE5FX
Miles Design LLC
Hi Mike,
The time rate does remain the same - at the device. The problem is the idea
that it is the hyperfine transitions that determine the time...
Hi John,
I hadn't run into this idea before, and I like it. But I have a problem with the statement:. "If you move through space at 100,000,000 meters per second in space, then your velocity in the t direction is 283,000,000 meters per second (because sqrt(100E6^2 + 283E6^2) = 300E6.)" The problem is that your velocity in the t direction remains the same to yourself, because your velocity as compared to yourself is always zero. So, yes, velocity with respect to some other object does change the rate of time as compared to that other object. But, as is understood from reading your whole post, time is always moving at the same rate for the one observing himself.
Bob
From: John Miles <john@miles.io>
To: 'Discussion of precise time and frequency measurement' time-nuts@febo.com
Sent: Friday, November 27, 2015 2:54 PM
Subject: Re: [time-nuts] Einstein Special on PBS
So, here's how I finally grokked this stuff. c, the speed of light in a vacuum, is often spoken of as a "speed limit" that nothing can ever exceed. That's a bad way to put it, and people who have expressed it that way in popular science writing for 100 years should feel bad.
Instead, the way to visualize relativity is to realize that c is the only speed at which anything can travel. You are always moving at 300,000,000 meters per second, whether you want to or not. But you're doing it through all four dimensions including time. If you choose to remain stationary in (x,y,z), then all of your velocity is in the t direction. If you move through space at 100,000,000 meters per second in space, then your velocity in the t direction is 283,000,000 meters per second (because sqrt(100E6^2 + 283E6^2) = 300E6.)
It doesn't make sense to speak of moving a certain number of "meters" through time, so your location in time itself is what has to change. You won't perceive any drift in your personal timebase when you move in space, any more than you will perceive a change in your location relative to yourself. ("No matter where you go, there you are.") But an independent observer will see a person who's moving at 100,000,000 meters per second in x,y,z and 283,000,000 meters per second in t. They see you moving in space, in the form of a location change, and they also see you moving in time, in the form of a disagreement between their perception of elapsed time and your own.
Likewise, if you spend all of your velocity allowance in (x,y,z), your t component is necessarily zero. Among other inconvenient effects that occur at dt/dt=0, you won't get any closer to your destination, even though your own watch is still ticking normally. Particles moving near c experience this effect from their point of view, even while we watch them smash into their targets at unimaginable speeds.
This is special relativity in action. The insight behind general relativity is twofold: 1) movement caused by the acceleration of gravity is indistinguishable from movement caused by anything else; and 2) you don't even have to move, just feel the acceleration. That second part was what really baked peoples' noodles. It is what's responsible for the disagreement between the two 5071As.
-- john, KE5FX
Miles Design LLC
Hi Mike,
The time rate does remain the same - at the device. The problem is the idea
that it is the hyperfine transitions that determine the time...
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
The mountain thing has been done.
Someone needs to take their
clock to the bottom of the deepest mine (2.4 miles).
Hi,
On 11/27/2015 05:03 PM, Tom Van Baak wrote:
They mentioned some "6 miles per day" offset due to GPS relativity effects.
I think this is the sum of both special relativity (time dilation) and
general relativity (gravitational) effects. The GR correction is 45
microseconds a day fast; the SR correction is 7 microseconds slow. 38
microseconds seconds is 11 kilometers which is indeed 6 or 7 miles. While
time drifts 38 microseconds a day, I'm not sure that GPS coordinates would
drift that fast - aren't most of the corrections in the same direction?
Hi Tim,
Correct. Here's from the "rel" program (in my http://leapsecond.com/tools/ folder):
C:\tvb\NPR>rel 20000km 14000kph
** Altitude 20000000.000 m (65616797.900 ft, 12427.424 mi) 5.274e-010 blueshift
1898630.424377 ps/hour
45567.130185 ns/day
** Velocity 3888.889 m/s (14000.000 km/h, 8699.197 mph) -8.414e-011 redshift
-302888.070815 ps/hour
-7269.313700 ns/day
** Net effect (GR+SR) 4.433e-010 shift
1595742.353562 ps/hour
38297.816485 ns/day
What this means is that as a source of UTC, GPS would in fact be off by 38 us per day if you forgot about relativity when you designed it.
But, you're right, you cannot blindly turn that "38 us/day" into "11 km/day". As long as all the GPS clocks are running too fast or too slow and as long as the receivers know what that offset is, the navigation system would still work just fine, relativity or not. This is true for any sort of triangulation (actually, trilateration) system.
GPS is a PNT (Position, Navigation, and Timing) system. So while GPS is really cool, and relativity is really cool, the navigation part of GPS does not "depend" on relativity, per-se.
As found in IS-GPS-200H:
http://www.gps.gov/technical/icwg/IS-GPS-200H.pdf
8<---
3.3.1.1 Frequency Plan.
For Block IIA, IIR, IIR-M, and IIF satellites, the requirements
specified in this IS shall pertain to the signal contained within two
20.46 MHz bands; one centered about the L1 nominal frequency
and the other centered about the L2 nominal frequency (see Table 3-Vb).
For GPS III and subsequent satellites, the requirements specified in
this IS shall pertain to the signal contained
within two 30.69 MHz bands; one centered about the L1 nominal frequency
and the other centered about the L2 nominal frequency (see Table 3-Vc).
The carrier frequencies for the L1 and L2 signals shall be coherently
derived from a common frequency source within the SV. The
nominal frequency of this source -- as it appears to an observer on the
ground -- is 10.23 MHz. The SV carrier frequency and clock rates --
as they would appear to an observer located in the SV -- are offset to
compensate for relativistic effects. The clock rates are offset by
∆ f/f = -4.4647E-10, equivalent to a change in the P-code chipping rate
of 10.23 MHz offset by a ∆f = -4.5674E-3 Hz. This is equal to
10.2299999954326 MHz. The nominal carrier frequencies (f0)
shall be 1575.42 MHz, and 1227.6 MHz for L1 and L2, respectively.
--->8
There is however relativistic effects that the user equipment must
compensate for, as it depends on the position of the user observation
and shifts will be different for each user or for that matter for the
user the shift will be different for each satellite.
Cheers,
Magnus
The trouble is that they experience different acceleration, due to
gravity, and this yanks the experienced time. In the relativistic world,
the concept of time is not consistent between locations, and the effect
of acceleration between two locations shift it, and this is a
consequence of a fixed speed of light. This is the consequences of fixed
speed of light, that the rate of time needs to shift and this is the
bizarreness of relativity that made many physics initially not accept
relativity. Over the 100 years, we have seen again and again that this
model actually makes sense for all the observations we have.
Elevating a clock from the earth, alters it's experienced gravitational
potential, the gravitational acceleration will be different. This is
similar to sending the clock towards us in a constant rate. Our
experience of their rate of time will be different, and so will they.
Our gravitational acceleration will from the top of the mountain look
like sending us away from them. For both cases the light speed is
constant, so we can only yank the rate of time, because the physics of
the clocks at each such location does not yank.
Think of the oscillators being modeled as
O1(t) = cos(2pif0T1(t))
O2(t) = cos(2pif0T2(t))
T1(t) and T2(t) being local time functions. With the clocks at the same
location or otherwise similar locations, these will be about the same.
The physics of the clock sets f0. It's only when we change the
characteristics that alter T1 and T2 that we can observe that
difference. The time t being here some arbitrary non-observable time.
Usually we get away with letting T1 and T2 be t directly, but the fixed
speed of light need us to alter these.
If you now take two clocks of different physics (Cs and H-maser) and
forms two pairs. One that stays and one that goes to the top. Each pair
will be consistent, to the degree they are for normal systematics, but
the mountain pair will both experience the same shift compared to the
valley pair.
Cheers,
Magnus
On 11/27/2015 07:10 PM, Mike Feher wrote:
Bob -
Thanks for attempting to make me see the light. But, I still do not. You said it yourself that hyperfine transitions remain the same. Since "time" on these device are derived from these transitions, they should also remain the same. I agree, from a relativistic point of vie the time will be different. I am just not convinced that using these types of clocks will demonstrate that. Thanks - Mike
Mike B. Feher, EOZ Inc.
89 Arnold Blvd.
Howell, NJ, 07731
732-886-5960 office
908-902-3831 cell
-----Original Message-----
From: time-nuts [mailto:time-nuts-bounces@febo.com] On Behalf Of Bob Stewart
Sent: Friday, November 27, 2015 12:48 PM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] Einstein Special on PBS
Hi Mike,
I'm far from an expert on this, but what you're missing is that time and space isn't the same between any two points that are located in different gravity gradients and/or moving at different relative velocities. The hyperfine transitions are happening at the same local rate whether the Cs device is on planet earth, in orbit around the earth, or in close proximity to the sun or even a black hole. But, all of these examples are happening in different space-time environments (i.e. different local frames), so that "relative" to each other, they are experiencing time at different rates.
It might help to think of it in terms of doppler effect, though this is not an exact comparison. But, if you have two clocks that are moving away from each other, they may very well be precisely synchronous, but because of the doppler effect, any measurement you make will show them to be running at different rates. Because of the effects of gravity, watches at different altitudes appear to run at different rates to the outsider, although to the person wearing the watch, nothing has actually changed; it is the other person's watch that is acting funny.
So, essentially, a clock sitting on the ground at sea level is running in a very slightly different space time than one that is sitting on a mountain. And when you place a clock in orbit, you also have 14,000 odd MPH of velocity that's also having an impact on the space-time of that object. As a result, when you bring the prodigal clock back to sea level, it will have experienced a slightly different amount of time than the one at sea level. Note that the prodigal clock hasn't run at a different rate. It has actually experienced time running at a different rate from that of the clock on the ground.
Bob
From: Mike Feher <mfeher@eozinc.com>
To: 'Discussion of precise time and frequency measurement' time-nuts@febo.com
Sent: Friday, November 27, 2015 9:37 AM
Subject: Re: [time-nuts] Einstein Special on PBS
I just do not get it. I know that now I am 70 and my good smart days are behind me, but, this should be simple. In all these clocks mentioned, time is derived from the transition of a hyperfine line of a certain atom within some element, in this case cesium, In order for any of these clocks to deviate in relative time at different heights for example, it seems to me that the period of the hyperfine transitions must change as well, to make the defined second longer or shorter. So, in these examples the elevation does not change the time, but the way the atoms behave. What obvious item am I missing, besides maybe brain capacity? Thanks - Mike
Mike B. Feher, EOZ Inc.
89 Arnold Blvd.
Howell, NJ, 07731
732-886-5960 office
908-902-3831 cell
-----Original Message-----
From: time-nuts [mailto:time-nuts-bounces@febo.com] On Behalf Of Tim Shoppa
Sent: Friday, November 27, 2015 9:19 AM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] Einstein Special on PBS
Would've been more fun to see Tom and his kids going to the top of Mt Ranier in 2005 with the ensemble :-). http://leapsecond.com/great2005/
They mentioned some "6 miles per day" offset due to GPS relativity effects.
I think this is the sum of both special relativity (time dilation) and general relativity (gravitational) effects. The GR correction is 45 microseconds a day fast; the SR correction is 7 microseconds slow. 38 microseconds seconds is 11 kilometers which is indeed 6 or 7 miles. While time drifts 38 microseconds a day, I'm not sure that GPS coordinates would drift that fast - aren't most of the corrections in the same direction?
Seeing Kip Thorne describe black holes was a blast - he refused to use the word mass when describing them, just like when I took a course from him in 1990. When my advisor taught the same course, I pleaded with him, "please use coordinates!". (Kip Thorne loves coordinate-free notation, unfortunately my brain does not work that way!!! I would've failed the course if it was only GR; fortunately it also had plasma physics in the same quarter, and I was an ace at that due to some undergraduate work.)
Tim N3QE
On Fri, Nov 27, 2015 at 12:05 AM, Arthur Dent golgarfrincham@gmail.com
wrote:
In the special it looks like they used two HP5071A standards, an
SRS620 counter, and a scope. They first made sure the stds were in
sync then took one to the building at the top of the ski lift on New
Hampshire's Mount Sunapee at 2726' elevation for 4 days where it would
be running a little faster because it would be slightly further from
the center of the spinning earth. After bringing the 5071A back from
the top of the mountain they checked the difference in the start of
square waves displayed on the scope and detected the 5071A at altitude
was now 20ns ahead of the 5071A kept at sea level, as predicted, if I
understood everything correctly. They explained that the clocks in the
GPS satellites traveling at a much higher speed had to correct for the
speed difference which also verified Einstein's theory.
My wife and I were on the top of Mt. Sunapee this summer where we
enjoyed the views but didn't run any experiments. ;-)
-Arthur
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Hi
….but …
As part of the time steering of the system, the ground segment constantly plays games with the
total correction of each SV. Even with no offset, they still would bring it all into alignment. Yes it
would be a major pain to do so with a “couple of mHz” error in the mix. I suspect that there are
some pretty involved corrections that take care of just about anything that can be calculated.
Bob
On Nov 28, 2015, at 5:16 AM, Magnus Danielson magnus@rubidium.dyndns.org wrote:
The trouble is that they experience different acceleration, due to gravity, and this yanks the experienced time. In the relativistic world, the concept of time is not consistent between locations, and the effect of acceleration between two locations shift it, and this is a consequence of a fixed speed of light. This is the consequences of fixed speed of light, that the rate of time needs to shift and this is the bizarreness of relativity that made many physics initially not accept relativity. Over the 100 years, we have seen again and again that this model actually makes sense for all the observations we have.
Elevating a clock from the earth, alters it's experienced gravitational potential, the gravitational acceleration will be different. This is similar to sending the clock towards us in a constant rate. Our experience of their rate of time will be different, and so will they. Our gravitational acceleration will from the top of the mountain look like sending us away from them. For both cases the light speed is constant, so we can only yank the rate of time, because the physics of the clocks at each such location does not yank.
Think of the oscillators being modeled as
O1(t) = cos(2pif0T1(t))
O2(t) = cos(2pif0T2(t))
T1(t) and T2(t) being local time functions. With the clocks at the same location or otherwise similar locations, these will be about the same. The physics of the clock sets f0. It's only when we change the characteristics that alter T1 and T2 that we can observe that difference. The time t being here some arbitrary non-observable time.
Usually we get away with letting T1 and T2 be t directly, but the fixed speed of light need us to alter these.
If you now take two clocks of different physics (Cs and H-maser) and forms two pairs. One that stays and one that goes to the top. Each pair will be consistent, to the degree they are for normal systematics, but the mountain pair will both experience the same shift compared to the valley pair.
Cheers,
Magnus
On 11/27/2015 07:10 PM, Mike Feher wrote:
Bob -
Thanks for attempting to make me see the light. But, I still do not. You said it yourself that hyperfine transitions remain the same. Since "time" on these device are derived from these transitions, they should also remain the same. I agree, from a relativistic point of vie the time will be different. I am just not convinced that using these types of clocks will demonstrate that. Thanks - Mike
Mike B. Feher, EOZ Inc.
89 Arnold Blvd.
Howell, NJ, 07731
732-886-5960 office
908-902-3831 cell
-----Original Message-----
From: time-nuts [mailto:time-nuts-bounces@febo.com] On Behalf Of Bob Stewart
Sent: Friday, November 27, 2015 12:48 PM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] Einstein Special on PBS
Hi Mike,
I'm far from an expert on this, but what you're missing is that time and space isn't the same between any two points that are located in different gravity gradients and/or moving at different relative velocities. The hyperfine transitions are happening at the same local rate whether the Cs device is on planet earth, in orbit around the earth, or in close proximity to the sun or even a black hole. But, all of these examples are happening in different space-time environments (i.e. different local frames), so that "relative" to each other, they are experiencing time at different rates.
It might help to think of it in terms of doppler effect, though this is not an exact comparison. But, if you have two clocks that are moving away from each other, they may very well be precisely synchronous, but because of the doppler effect, any measurement you make will show them to be running at different rates. Because of the effects of gravity, watches at different altitudes appear to run at different rates to the outsider, although to the person wearing the watch, nothing has actually changed; it is the other person's watch that is acting funny.
So, essentially, a clock sitting on the ground at sea level is running in a very slightly different space time than one that is sitting on a mountain. And when you place a clock in orbit, you also have 14,000 odd MPH of velocity that's also having an impact on the space-time of that object. As a result, when you bring the prodigal clock back to sea level, it will have experienced a slightly different amount of time than the one at sea level. Note that the prodigal clock hasn't run at a different rate. It has actually experienced time running at a different rate from that of the clock on the ground.
Bob
From: Mike Feher <mfeher@eozinc.com>
To: 'Discussion of precise time and frequency measurement' time-nuts@febo.com
Sent: Friday, November 27, 2015 9:37 AM
Subject: Re: [time-nuts] Einstein Special on PBS
I just do not get it. I know that now I am 70 and my good smart days are behind me, but, this should be simple. In all these clocks mentioned, time is derived from the transition of a hyperfine line of a certain atom within some element, in this case cesium, In order for any of these clocks to deviate in relative time at different heights for example, it seems to me that the period of the hyperfine transitions must change as well, to make the defined second longer or shorter. So, in these examples the elevation does not change the time, but the way the atoms behave. What obvious item am I missing, besides maybe brain capacity? Thanks - Mike
Mike B. Feher, EOZ Inc.
89 Arnold Blvd.
Howell, NJ, 07731
732-886-5960 office
908-902-3831 cell
-----Original Message-----
From: time-nuts [mailto:time-nuts-bounces@febo.com] On Behalf Of Tim Shoppa
Sent: Friday, November 27, 2015 9:19 AM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] Einstein Special on PBS
Would've been more fun to see Tom and his kids going to the top of Mt Ranier in 2005 with the ensemble :-). http://leapsecond.com/great2005/
They mentioned some "6 miles per day" offset due to GPS relativity effects.
I think this is the sum of both special relativity (time dilation) and general relativity (gravitational) effects. The GR correction is 45 microseconds a day fast; the SR correction is 7 microseconds slow. 38 microseconds seconds is 11 kilometers which is indeed 6 or 7 miles. While time drifts 38 microseconds a day, I'm not sure that GPS coordinates would drift that fast - aren't most of the corrections in the same direction?
Seeing Kip Thorne describe black holes was a blast - he refused to use the word mass when describing them, just like when I took a course from him in 1990. When my advisor taught the same course, I pleaded with him, "please use coordinates!". (Kip Thorne loves coordinate-free notation, unfortunately my brain does not work that way!!! I would've failed the course if it was only GR; fortunately it also had plasma physics in the same quarter, and I was an ace at that due to some undergraduate work.)
Tim N3QE
On Fri, Nov 27, 2015 at 12:05 AM, Arthur Dent golgarfrincham@gmail.com
wrote:
In the special it looks like they used two HP5071A standards, an
SRS620 counter, and a scope. They first made sure the stds were in
sync then took one to the building at the top of the ski lift on New
Hampshire's Mount Sunapee at 2726' elevation for 4 days where it would
be running a little faster because it would be slightly further from
the center of the spinning earth. After bringing the 5071A back from
the top of the mountain they checked the difference in the start of
square waves displayed on the scope and detected the 5071A at altitude
was now 20ns ahead of the 5071A kept at sea level, as predicted, if I
understood everything correctly. They explained that the clocks in the
GPS satellites traveling at a much higher speed had to correct for the
speed difference which also verified Einstein's theory.
My wife and I were on the top of Mt. Sunapee this summer where we
enjoyed the views but didn't run any experiments. ;-)
-Arthur
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Wow. So elegantly simple explanation, thanks John!
On November 27, 2015 2:54:51 PM CST, John Miles john@miles.io wrote:
So, here's how I finally grokked this stuff. c, the speed of light in
a vacuum, is often spoken of as a "speed limit" that nothing can ever
exceed. That's a bad way to put it, and people who have expressed it
that way in popular science writing for 100 years should feel bad.
Instead, the way to visualize relativity is to realize that c is the
only speed at which anything can travel. You are always moving at
300,000,000 meters per second, whether you want to or not. But you're
doing it through all four dimensions including time. If you choose to
remain stationary in (x,y,z), then all of your velocity is in the t
direction. If you move through space at 100,000,000 meters per second
in space, then your velocity in the t direction is 283,000,000 meters
per second (because sqrt(100E6^2 + 283E6^2) = 300E6.)
It doesn't make sense to speak of moving a certain number of "meters"
through time, so your location in time itself is what has to change.
You won't perceive any drift in your personal timebase when you move in
space, any more than you will perceive a change in your location
relative to yourself. ("No matter where you go, there you are.") But
an independent observer will see a person who's moving at 100,000,000
meters per second in x,y,z and 283,000,000 meters per second in t.
They see you moving in space, in the form of a location change, and
they also see you moving in time, in the form of a disagreement between
their perception of elapsed time and your own.
Likewise, if you spend all of your velocity allowance in (x,y,z), your
t component is necessarily zero. Among other inconvenient effects that
occur at dt/dt=0, you won't get any closer to your destination, even
though your own watch is still ticking normally. Particles moving near
c experience this effect from their point of view, even while we watch
them smash into their targets at unimaginable speeds.
This is special relativity in action. The insight behind general
relativity is twofold: 1) movement caused by the acceleration of
gravity is indistinguishable from movement caused by anything else; and
2) you don't even have to move, just feel the acceleration. That
second part was what really baked peoples' noodles. It is what's
responsible for the disagreement between the two 5071As.
-- john, KE5FX
Miles Design LLC
Hi Mike,
The time rate does remain the same - at the device. The problem is
the idea
that it is the hyperfine transitions that determine the time...
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to
https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
--
Sent from my Moto-X wireless tracker while I do other things.
Hi John,
Thank you very much for this explanation, I found it very "explicative".
What I am not able to grasp is the sense of the phrase " That second
part was what really baked peoples' noodles". I think that is some
colloquial but not being English my native language I can't figure out
its meaning.
Thank you,
Ignacio
El 27/11/2015 a las 21:54, John Miles wrote:
So, here's how I finally grokked this stuff. c, the speed of light in a vacuum, is often spoken of as a "speed limit" that nothing can ever exceed. That's a bad way to put it, and people who have expressed it that way in popular science writing for 100 years should feel bad.
Instead, the way to visualize relativity is to realize that c is the only speed at which anything can travel. You are always moving at 300,000,000 meters per second, whether you want to or not. But you're doing it through all four dimensions including time. If you choose to remain stationary in (x,y,z), then all of your velocity is in the t direction. If you move through space at 100,000,000 meters per second in space, then your velocity in the t direction is 283,000,000 meters per second (because sqrt(100E6^2 + 283E6^2) = 300E6.)
It doesn't make sense to speak of moving a certain number of "meters" through time, so your location in time itself is what has to change. You won't perceive any drift in your personal timebase when you move in space, any more than you will perceive a change in your location relative to yourself. ("No matter where you go, there you are.") But an independent observer will see a person who's moving at 100,000,000 meters per second in x,y,z and 283,000,000 meters per second in t. They see you moving in space, in the form of a location change, and they also see you moving in time, in the form of a disagreement between their perception of elapsed time and your own.
Likewise, if you spend all of your velocity allowance in (x,y,z), your t component is necessarily zero. Among other inconvenient effects that occur at dt/dt=0, you won't get any closer to your destination, even though your own watch is still ticking normally. Particles moving near c experience this effect from their point of view, even while we watch them smash into their targets at unimaginable speeds.
This is special relativity in action. The insight behind general relativity is twofold: 1) movement caused by the acceleration of gravity is indistinguishable from movement caused by anything else; and 2) you don't even have to move, just feel the acceleration. That second part was what really baked peoples' noodles. It is what's responsible for the disagreement between the two 5071As.
-- john, KE5FX
Miles Design LLC
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Chris,
A few years after my Mt Rainier trip I looked into doing the same experiment down a mine. But besides having mountains Seattle also has the Pacific ocean so there are any number of commercial and research deep sea operations around here. I thought it would fun to put a few 5071A and batteries into a bathysphere and send them down as many thousand feet as possible for a couple of days.
One advantage is that many of them have long fiber data links and so I thought it might be possible to compare clocks live during the experiment instead of having to wait for the round-trip. TDR could be used to compensate for fiber tempco.
The theory is simple. Below sea level gravity falls by 1/r and above sea level gravity falls by 1/r^2. The magic number, W0, is -6.969e-10 which how slow Earth's SI second is compared to "free space". In other words, clocks speed up on either side of mean sea level. Yes, an atomic clock can be used as a depth gauge as well as an altimeter.
You're probably thinking it would be fun to detect the difference between 1/r and 1/r^2 effects. But the problem is that the earth has a radius of 3900 miles so for a couple of miles above or below the surface, 1/r and 1/r^2 look identical. That is, you get the same blueshift: 1.1e-16/meter.
/tvb
----- Original Message -----
From: "Chris Howard" chris@elfpen.com
To: time-nuts@febo.com
Sent: Friday, November 27, 2015 7:04 PM
Subject: Re: [time-nuts] Einstein Special on PBS
The mountain thing has been done.
Someone needs to take their
clock to the bottom of the deepest mine (2.4 miles).
It's not exactly a rigorous explanation, but I think it's a good memory aid. Once you realize that c is a 4D constant rather than a scalar speed, you can work out for yourself which way clock measurements are skewed from various points of view.
-- john, KE5FX
-----Original Message-----
From: time-nuts [mailto:time-nuts-bounces@febo.com] On Behalf Of Didier
Juges
Sent: Sunday, November 29, 2015 11:20 AM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] Einstein Special on PBS
Wow. So elegantly simple explanation, thanks John!
On November 27, 2015 2:54:51 PM CST, John Miles john@miles.io wrote:
So, here's how I finally grokked this stuff. c, the speed of light in
a vacuum, is often spoken of as a "speed limit" that nothing can ever
exceed. That's a bad way to put it, and people who have expressed it
that way in popular science writing for 100 years should feel bad.