Why Aren’t ALL SR Effects Cumulative?

[MacWylie]

TL;DR Summary

Example: the Lorentz Contraction goes away when v—>0 but Time Dilation does not.

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing. Clearly, Space and Time are not treated on an equal footing or the times in both frames would snap back in sync just like the lengths do. I’m referring to 2 frames in relative motion v and comparing the Lorentz Contraction and Time Dilation. Thank you.

 

[Ibix]

Clearly, Space and Time are not treated on an equal footing or the times in both frames would snap back in sync just like the lengths do.

If you accelerate and then slow down again then your clocks will tick at the same rate as those you left behind, just with an offset zero. Similarly, rulers will show the same distance between their graduations as those you left behind, but with an offset origin (unless you turn around and carefully reset the ruler origins to match).

 

[PeroK]

Summary:: Example: the Lorentz Contraction goes away when v—>0 but Time Dilation does not.

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing. Clearly, Space and Time are not treated on an equal footing or the times in both frames would snap back in sync just like the lengths do. I’m referring to 2 frames in relative motion v and comparing the Lorentz Contraction and Time Dilation. Thank you.

If you have a clock that ticks but doesn't record anything permanent, then it does the same as a ruler in the sense that its measured tick rate is varies with its relative velocity.

The difference between a clock and a ruler is that most clocks record something permanent.

The difference between time and space is the sign in the spacetime distance: $$ds^2 = c^2 dt^2 - dx^2 - dy^2 -dz^2$$ Time is not, therefore, just another spatial dimension. That's the trouble with phrases like "equal footing".

 

[MacWylie]

If you accelerate and then slow down again then your clocks will tick at the same rate as those you left behind, just with an offset zero. Similarly, rulers will show the same distance between their graduations as those you left behind, but with an offset origin (unless you turn around and carefully reset the ruler origins to match).

The bottom line is there will be agreement on the length of an object BUT there will never be agreement on what time it is. Someone is now less old. That makes Time and Space as separate and NOT equal.

 

[PeroK]

The bottom line is there will be agreement on the length of an object BUT there will never be agreement on what time it is.

Those are two completely different things. One is a specific physical object; the other is an arbitrary time coordinate.

 

[Ibix]

The bottom line is there will be agreement on the length of an object BUT there will never be agreement on what time it is. Someone is now less old. That makes Time and Space as separate and NOT equal.

As @PeroK points out, you're comparing apples and oranges. A fair comparison would be elapsed time versus total distance traveled by the traveller (perhaps measured with his car's odometer and compared to an integral of his speed measured by Doppler radar in the ground frame). There would be permanent difference in those displacements.

 

[MacWylie]

As @PeroK points out, you're comparing apples and oranges. A fair comparison would be elapsed time versus total distance traveled by the traveller (perhaps measured with his car's odometer and compared to an integral of his speed measured by Doppler radar in the ground frame). There would be permanent difference in those displacements.

That’s my point. Space and Time are NOT treated equally in Special Relativity as the dogma goes.

 

[Vanadium 50]

Dogma? Why are you using such a loaded word?

 

[Sagittarius A-Star]

Summary:: Example: the Lorentz Contraction goes away when v—>0 but Time Dilation does not.

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing.

A clock has a built-in memory. Also, an odometer in a car has a built-in memory. Assume, one twin is driving with a car from Earth via the new highway to alpha-centauri and back. At arrival, his odometer will show the length-contracted distance to and from alpha-centauri.

 

[Ibix]

That’s my point. Space and Time are NOT treated equally in Special Relativity as the dogma goes.

I'm not sure what you mean. You seem to be pointing out that a device with a memory does not behave like a device without a memory. We're aware of that. If you use the devices in the same way (ignoring their memories) they are equivalent, at least in 1+1d. It gets a bit more complex in more dimensions, but then there's more than one spacelike dimension and still only one timelike dimension, so describing them as "equivalent" would be a stretch.

I'm not sure what you think is "dogma" here. I suspect you've been reading popsci sources, which don't necessarily reflect scientific theories terribly well. It's best to treat them with the same caution as an "inspired by a true story" movie.

 

[MacWylie]

All I’m saying is the effects of the Lorentz Contraction are reversible and the effects of Time Dilation are not.

 

[Sagittarius A-Star]

All I’m saying is the effects of the Lorentz Contraction are reversible and the effects of Time Dilation are not.

No. You can modify/manipulate both, the odometer-memory content and the clock-memory content.

 

[A.T.]

All I’m saying is the effects of the Lorentz Contraction are reversible and the effects of Time Dilation are not.

Only if you define "effects of" differently.

 

[MacWylie]

I'm not sure what you mean. You seem to be pointing out that a device with a memory does not behave like a device without a memory. We're aware of that. If you use the devices in the same way (ignoring their memories) they are equivalent, at least in 1+1d. It gets a bit more complex in more dimensions, but then there's more than one spacelike dimension and still only one timelike dimension, so describing them as "equivalent" would be a stretch.

I'm not sure what you think is "dogma" here. I suspect you've been reading popsci sources, which don't necessarily reflect scientific theories terribly well. It's best to treat them with the same caution as an "inspired by a true story" movie.

No, once again, all I’m saying is when the relative velocity goes back to zero the there is no more Lorentz Contraction as if there never ever was ever. But, Time Dilation also goes back to zero BUT there is a HUGE non-reversible effect a la Twin Paradox.

 

[Ibix]

No, once again, all I’m saying is when the relative velocity goes back to zero the there is no more Lorentz Contraction as if there never ever was ever. But, Time Dilation also goes back to zero BUT there is a HUGE non-reversible effect a la Twin Paradox.

But that is not time dilation. That is differential aging. That is something you can only detect because the clock has a memory which the ruler does not. You can detect "differential distance" with an odometer (which has a memory) - and that will be non-reversible.

You don't seem to be catching the distinction that is being made by us.

 

[Sagittarius A-Star]

No, once again, all I’m saying is when the relative velocity goes back to zero the there is no more Lorentz Contraction as if there never ever was ever. But, Time Dilation also goes back to zero BUT there is a HUGE non-reversible effect a la Twin Paradox.

If the traveling twin is only an ideal metronome without memory (=no aging effects), then after arrival (with v -> 0) the metronome ticks at "normal" rate, as if there never ever was a time dilation.

 

[MacWylie]

Yeah, I understand what you’re saying but you’re not understanding what I’m saying: the spatial vs time effects from SR are not equal. That’s it.

 

[tomdodd4598]

This thread might be evidence that time loops into the past are indeed possible.

 

[Sagittarius A-Star]

I’m saying: the spatial vs time effects from SR are not equal. That’s it.

That's a more unspecific statement than what you said before. Before that you said, that time dilation is cumulative and length contraction is not. But cumulative are only the measurement devices with a built-in counter, like odometer or clock/human.

 

[Ibix]

Yeah, I understand what you’re saying but you’re not understanding what I’m saying: the spatial vs time effects from SR are not equal. That’s it.

But you keep trying to support the claim by comparing the readings on devices with a memory to the readings on devices without memories. The latter cannot remember their history of movement. The former can. So of course their behaviour is different. If you replace the clocks with metronomes (as @Sagittarius A-Star suggests) or the rulers with odometers (as I suggest) then the different behaviours disappear.

There are differences between space and time, but they have to do with space having three dimensions and time only one. This is not something you can analyse with a single clock and a ruler.

 

[Nugatory]

No, once again, all I’m saying is when the relative velocity goes back to zero the there is no more Lorentz Contraction as if there never ever was ever. But, Time Dilation also goes back to zero BUT there is a HUGE non-reversible effect a la Twin Paradox.

There is an analogous non-reversible effect on distances. Say we have a car instead of a spaceship, so that we can install an odometer that ticks off one kilometer for every kilometer of road that passes under the wheels (note that in the spirit of special relativity, this description works whether we consider the car to be at rest while the road moves, or the car to be moving over a stationary road). We will also dispense with the dashboard clock on the car and instead use the twins' heartrate as a clock (assume their hearts beat once per second according to them - if it is not clear to you that this assumption is unaffected by time dilation we'll have to back up and address a more basic but very common misunderstanding) so that we can have a direct connection between our time measurements and the age of the twins.

At the end of the trip, the car's odometer, measuring the spatial distance of the journey, will read fewer kilometers than the spatial length of the journey according to the stay-at-home twin's measurement of the distance traveled. The traveling twin's heart will have beaten fewer times than the stay-at-home twin's heart, so the temporal length of the journey was less also for the traveller than for the stay-at-home twin. Both effects are non-reversible - "too few" heartbeats and "too few" kilometers under the wheels, and once the twins are back at rest relative to one another both the "missing" heartbeats and the "missing" kilometers are missing forever.

 

[Nugatory]

That’s my point. Space and Time are NOT treated equally in Special Relativity as the dogma goes.

Space and time are indeed different things: Time is what a clock measures and space is what a ruler measures.

The "dogma" that you are referring to doesn't mean what you're thinking it does - and you should always be cautious about taking things that are stated in natural language instead of math too seriously. Natural language is just not precise enough to avoid the sorts of ambiguities that are misleading you here.

(Free advice - a few days of quality time with Taylor and Wheeler's "Spacetime Physics" will help correct many of the misconceptions people pick up from popular presentations).

 

[A.T.]

Yeah, I understand what you’re saying but you’re not understanding what I’m saying: the spatial vs time effects from SR are not equal. That’s it.

What you were saying was vague, and now you have made made it even more vague. You are moving in the wrong direction in terms of thinking precisely.

 

[stevendaryl]

The bottom line is there will be agreement on the length of an object BUT there will never be agreement on what time it is. Someone is now less old. That makes Time and Space as separate and NOT equal.

The question "What time is it?" is not analogous to "How long is this stick?". It's more analogous to "What is the x-coordinate of the end of this stick?"

Here's a Euclidean analogy to the "paradox":

You have two highways running parallel from west to east, with Highway B to the north of highway A. On each highway, there are markers showing distance along that highway, one marker every 10 meters, labeled with positive integers. On the western end of Highway B, the markers are synchronized: Marker number 1 of Highway B is directly to the north of marker number 1 of Highway A. At some point, Highway B makes a turn to the northeast, and separates from Highway A. At a point farther to the east, Highway B makes another turn to the southeast, and comes back toward Highway A. After that point, the two highways are again parallel.

Would you expect that the markers for the two highways to still be synchronized? No, even after they become parallel again, the markers on the two highways will show different numbers. The marker number doesn't just reflect current conditions of the highway, but also information about the past for that highway.

 

[Janus]

No, once again, all I’m saying is when the relative velocity goes back to zero the there is no more Lorentz Contraction as if there never ever was ever.

If you travel to a star 6 ly distant ( as measured from Earth) at 0.6 c, it takes 10 yrs according to the Earth while your clock will record just 8 yrs.
By Earth's measurements, this is because you were time dilated. But, by your measurements it is because the distance between Earth and planet are length contracted to just 4.8 ly. Even once you stop at the planet, and the distance as measured by you goes to 6 ly, the affects of it being just 4.8 ly remain. They do not go away as if there had been no length contraction at all. If you had carried a device that measured the trip length, it will have recorded a distance of 4.8 ly, and will not "reset" to 6 ly once you stop.

 

[Grasshopper]

Clocks: don’t magically re-sync when they are brought back together.

Odometers: don’t magically re-sync when they are brought back together.

What’s the impossible difference here that shatters all the “dogma” that the foolish physicists have failed to see through again?

 

[anuttarasammyak]

Summary:: Example: the Lorentz Contraction goes away when v—>0 but Time Dilation does not.
Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing.

I do not catch your point. Say there are two IFRs, we call them A and B, with relative speed in z direction
In IFR A, z measure of B contracts and clock of B paces slower.
In IFR B, z measure of A contracts and clock of A paces slower.
You are claiming about this symmetry?

 

[PeterDonis]

The bottom line is there will be agreement on the length of an object BUT there will never be agreement on what time it is.

But there will be agreement on how much time passed along particular worldlines between two particular events. That is what is analogous to "length of an object".

"What time it is" is analogous to "how much distance is there between some particular object's location and the spatial origin of coordinates". And, as has already been pointed out, your spatial origin of coordinates does change if you accelerate and then slow down again, relative to some fixed object.

So in fact there is symmetry in both of these things; you just have to correctly understand what the things are in each case.

 

[Dale]

Yeah, I understand what you’re saying but you’re not understanding what I’m saying: the spatial vs time effects from SR are not equal. That’s it.

You are incorrect. If you use a metronome and a ruler the spatial and the time effects are the same. If you use an odometer and a clock the spatial and the time effects are the same. If you use a clock and a ruler or if you use a metronome and an odometer then the effects are different as you have pointed out.

The difference is not in space or time nor is it in the theory. Instead, it is only in the devices that you have used. If you use analogous devices then you get analogous results if you use non-analogous devices then you get non-analogous results.

Btw, there are indeed important differences between time and space, so it is not correct to assume that everything should be identical between them. But the difference you have described is not one.