Relativity and the question of age

[Naveen3456]

Suppose our galaxy, say A, is moving at near the speed of light with respect to another galaxy, say B. (which I think it indeed is doing ).

My age is say 80 years in my position (at earth, in the solar system, in the galaxy).

1. Persons in the 'another' galaxy are doing experiments regarding my age. they see me grow day by day but in their galaxy generations pass before I die. It's because as compared to them my time has slowed down extremely.

Now, my galaxy may be at rest as compared to some yet another galaxy, say C. There people will find my age to be just 80 years only.

So, what is my correct age/ Can someone measure it be less than 80 years? How?

2. When my 'time' slows down for galaxy B, do the motions of electrons around the atoms that constitute my body also slow down? How is matter or life possible in such a case. Won't the electrons fall inside the nucleus (relative to the person who is seeing me from galaxy B).

How can we be so sure that if the motion of the cells of our body, the chemical reactions taking place in them, and all the processes of our body like heartbeat etc. slow down (even if relative to another), we will continue to live. Won't the person who is viewing us from galaxy B see us dead and even .disintegrated

 

[Mentz114]

Suppose our galaxy, say A, is moving at near the speed of light with respect to another galaxy, say B. (which I think it indeed is doing ).

My age is say 80 years in my position (at earth, in the solar system, in the galaxy).

1. Persons in the 'another' galaxy are doing experiments regarding my age. they see me grow day by day but in their galaxy generations pass before I die. It's because as compared to them my time has slowed down extremely.

Now, my galaxy may be at rest as compared to some yet another galaxy, say C. There people will find my age to be just 80 years only.

So, what is my correct age/ Can someone measure it be less than 80 years? How?

2. When my 'time' slows down for galaxy B, do the motions of electrons around the atoms that constitute my body also slow down? How is matter or life possible in such a case. Won't the electrons fall inside the nucleus (relative to the person who is seeing me from galaxy B).

How can we be so sure that if the motion of the cells of our body, the chemical reactions taking place in them, and all the processes of our body like heartbeat etc. slow down (even if relative to another), we will continue to live. Won't the person who is viewing us from galaxy B see us dead and even .disintegrated

What happens to you cannot be affected by the fact that you are being watched by these extra-galactic observed. Your constituent electrons will behave exactly as they should.

Your age is always what the clocks and calendars say in your local frame, and all observers will agree on that.

 

[DiracPool]

2. When my 'time' slows down for galaxy B, do the motions of electrons around the atoms that constitute my body also slow down? How is matter or life possible in such a case. Won't the electrons fall inside the nucleus (relative to the person who is seeing me from galaxy B).

How can we be so sure that if the motion of the cells of our body, the chemical reactions taking place in them, and all the processes of our body like heartbeat etc. slow down (even if relative to another), we will continue to live. Won't the person who is viewing us from galaxy B see us dead and even .disintegrated

That's an excellent question, Naveen, and very legitimate. What you are making, though, is a classic "category mistake" by assuming that only the motions of the electrons in atoms are going to be affected by this time dilation, while everything else behaves normally. What actually happens is that ALL of the physical and physiological systems are slowed down proportionally to one another so the global systemic operation is unchanged. I'll admit I'm not sure if we are to take these slowed down physiological processes as really occurring and functioning in a slowed down time, or that they are really occurring the "normal" time frame for you (A), and the slowing down of those physiological processes is simply an optical illusion given to those in galaxy B. Perhaps a relativist in this forum can enlighten us.

Whatever the case, though, the reason that these processes are allowed to continue and DO continue, is that everything is functioning normally in your rest frame, regardless of what's going on in B's rest frame. B is just witnessing the normality of the physiological processes in your frame.

 

[soothsayer]

Also, our galaxy is not, in fact, moving near the speed of light with respect to any galaxies. You may be thinking of the expansion of space between our galaxy and distant ones, but that is different, and doesn't involve time dilation.

 

[Naty1]

I'll admit I'm not sure if we are to take these slowed down physiological processes as really occurring and functioning in a slowed down time, or that they are really occurring the "normal" time frame for you (A), and the slowing down of those physiological processes is simply an optical illusion given to those in galaxy B. Perhaps a relativist in this forum can enlighten us.

Mentz already answered this in the prior post. Local clocks, for example, tick at a steady even pace.

What is 'real' locally is not necessarily what is 'real' from a distant frame of reference. It is not an 'optical illusion'...bring different clocks together in the twin paradox and sure enough they have ticked off comparatively different times...but each maintains it's proper time in it's local frame.

A simple example: You view a friend alongside a distant house...gee they look so small...but so do you from their perspective...what is the 'real' size of each of you? Which view is 'real'??
And in this example, there is not even any time nor relative motion...just as simplistic an example as I can suggest.

 

[DiracPool]

What is 'real' locally is not necessarily what is 'real' from a distant frame of reference. It is not an 'optical illusion'...bring different clocks together in the twin paradox and sure enough they have ticked off comparatively different times...but each maintains it's proper time in it's local frame.

Yeah, and this continues to be the problem with the twin paradox that drives lesser mortals crazy. Your statement is even paradoxical, even though you're asserting it to be otherwise.

What is 'real' locally is not necessarily what is 'real' from a distant frame of reference.

Well, if my twin shows up after his "trip" younger than me than the fact that his physiological processes were slowed relative to mine is real. But they weren't slowed down for him, right? So how do you reconcile that? At what rate were his physiological processes actually occurring at? To say it depends on your frame of reference doesn't add up for me. It seems as if you're having it both ways.

So then the OP's concern comes back into frame (no pun intended). Are physiological processes scale invariant? Can we take the rate of the reactions of cellular respiration, cut them in half proportionally across the board, and everything still works as normal? Perhaps... Any cryogenecists want to chime in?

 

[Nugatory]

Well, if my twin shows up after his "trip" younger than me than the fact that his physiological processes were slowed relative to mine is real. But they weren't slowed down for him, right? So how do you reconcile that? At what rate were his physiological processes actually occurring at? To say it depends on your frame of reference doesn't add up for me. It seems as if you're having it both ways.

The twin paradox doesn't come from frames of reference, it comes from the path that each twin takes through spacetime.

I and my twin shake hands, get into our cars, set the odometers of our cars to zero, then drive off at a constant speed (as indicated by our speedometers) of 100 km/hr on different routes. Some hours later we meet in a distant city (my twin arrives there before me and waits for me to show up), swear under oath that were driving at 100 km/hr the whole time between our departure and our arrival at the destination... Yet the odometer of my car reads a higher value than the odometer of my twin's car. There's no great mystery here, I just took a longer route through space than my twin did.

The twin paradox is the same thing except with spacetime instead of space, so not only do we record a different distance traveled, we also record a different time elapsed.

 

[Naveen3456]

A simple example: You view a friend alongside a distant house...gee they look so small...but so do you from their perspective...what is the 'real' size of each of you? Which view is 'real'??
And in this example, there is not even any time nor relative motion...just as simplistic an example as I can suggest.

Why does the house at a distance appear small?

A person is standing near a house. Light bounces off the house and enters his eyes with all the information about the house and he sees the particular 'size' of the house.

Now, he retreats 500 meters back. Light is still reaching his eyes with all the information about the house. The distance that light has traveled is miniscule (500m) as compares to its speed (300000 km/s). The intensity of the light also has not diminished.

So, the person should be getting the same information about the house and its size should also be same from that small distance.

What actually is happening here?

Just a bit of 'useless' thinking on my part.

 

[Naveen3456]

The twin paradox doesn't come from frames of reference, it comes from the path that each twin takes through spacetime.

I and my twin shake hands, get into our cars, set the odometers of our cars to zero, then drive off at a constant speed (as indicated by our speedometers) of 100 km/hr on different routes. Some hours later we meet in a distant city (my twin arrives there before me and waits for me to show up), swear under oath that were driving at 100 km/hr the whole time between our departure and our arrival at the destination... Yet the odometer of my car reads a higher value than the odometer of my twin's car. There's no great mystery here, I just took a longer route through space than my twin did.

The twin paradox is the same thing except with spacetime instead of space, so not only do we record a different distance traveled, we also record a different time elapsed.

In your example, speed is same where as time and distance are different. This is understandable.

But in the twin paradox case, not only is speed different but time, distance( length contraction), mass (increase in mass), KE, age etc. are different. This is a completely bizarre scenario. Everything is different.

 

[DiracPool]

A person is standing near a house. Light bounces off the house and enters his eyes with all the information about the house and he sees the particular 'size' of the house.

Now, he retreats 500 meters back. Light is still reaching his eyes with all the information about the house. The distance that light has traveled is miniscule (500m) as compares to its speed (300000 km/s). The intensity of the light also has not diminished.

The intensity of the light has diminished, it falls off as the square of the distance of the person from the house.
http://csep10.phys.utk.edu/astr162/lect/light/intensity.html

So, the person should be getting the same information about the house and its size should also be same from that small distance

No it shouldn't. The person is farther away. The house is going to appear smaller. This is an issue of optics and perspective, it has nothing to do with relativity and the twin paradox.

What actually is happening here?

See above.

 

[Nugatory]

In your example, speed is same where as time and distance are different. This is understandable.

But in the twin paradox case, not only is speed different but time, distance( length contraction), mass (increase in mass), KE, age etc. are different. This is a completely bizarre scenario. Everything is different.

It gets a lot less bizarre if you draw a space-time diagram showing the two twin's paths through space-time and then calculate the length of each path.

 

[Naveen3456]

It gets a lot less bizarre if you draw a space-time diagram showing the two twin's paths through space-time and then calculate the length of each path.

OK, I agree that only maths can help me out here. No common sensical picture is going to help.

But how would the twin who is on Earth reconcile to what is happening on the spaceship that his twin is in.

He wouldn't be able to recognize his twin's face/body due to length contraction. There is a billiards table in the space ship, it would appear squeezed or warped. Everything in the spaceship would be beyond recognition/warped.

How would he understand that extremely low 'heart beat' on Earth is a sign of 'extreme weakness' and even death, but his twin is hale and hearty with such a slowed down heartbeat or lung function or the like. How will he understand that everything is happening in 'slow motion' in the space ship?

Then, if we tell him that laws of physics are same for you as well as for your twin/spaceship, how is he going to understand/compute/theorize all this.


It is assumed that the spaceship is moving near the speed of light in uniform motion with respect to earth, the home of first twin.

 

[Mentz114]

OK, I agree that only maths can help me out here. No common sensical picture is going to help.

But how would the twin who is on Earth reconcile to what is happening on the spaceship that his twin is in.

He wouldn't be able to recognize his twin's face/body due to length contraction. There is a billiards table in the space ship, it would appear squeezed or warped. Everything in the spaceship would be beyond recognition/warped.

How would he understand that extremely low 'heart beat' on Earth is a sign of 'extreme weakness' and even death, but his twin is hale and hearty with such a slowed down heartbeat or lung function or the like. How will he understand that everything is happening in 'slow motion' in the space ship?

Then, if we tell him that laws of physics are same for you as well as for your twin/spaceship, how is he going to understand/compute/theorize all this.


It is assumed that the spaceship is moving near the speed of light in uniform motion with respect to earth, the home of first twin.

If the distant twin sends a video recording of himself that lasts an hour on his clock ( ie a certain number of frames) then the receiving twin, using the correct video protocol will see everything is normal. The video would last one hour on his clock also.

 

[Naty1]

Yeah, and this continues to be the problem with the twin paradox that drives lesser mortals crazy. Your statement is even paradoxical, even though you're asserting it to be otherwise.

In relativity it is not paradoxical; in Newtonian physics it sure is considered 'paradoxical'.

It appears as such because none of us are used to observing such phenomena and we are not taught about the variable nature of space and time. [like velocities not directly adding at relativistic speeds]
It is time and space that are dynamic variables, not immutable constants, and they sure do NOT appear to be that way in our everyday experience. THAT is the root cause of 'paradoxical' here.[ We also tend to 'think' things are deterministic when in fact they are probabilistic [as in quantum mechanics]...so nature again confounds us! see my signature...Nature IS bizzare!]

Why does the house at a distance appear small?

Well if you are going to take my simplistic example too far, it flops! But it is simply a lense [focus] type effect...nothing much really to do with relativity...

The twin paradox doesn't come from frames of reference, it comes from the path that each twin takes through spacetime.

This of course is a better way to explain some things that I did, but it doesn't seem to satisfy. Taking this one step further, geodesic paths [worldines], are the shortest paths between any two events, with distance being defined in terms of spacetime intervals:

There's no great mystery here, I just took a longer route through space than my twin did. The twin paradox is the same thing except with spacetime instead of space, so not only do we record a different distance traveled, we also record a different time elapsed.

yes...and a precise way to think about this is that when one twin 'powers up' and rides 'faster in space' [as Nugatory describes]...they take a LONGER spacetime route. Why is this: the distance metric contains opposite signs for time and space, if space is bigger, time is smaller. [Of course none of this really explains WHY it happens; we know it follows such math from observational confirmation of relativity. ]

 

[jartsa]

Then, if we tell him that laws of physics are same for you as well as for your twin/spaceship, how is he going to understand/compute/theorize all this.

Well you never hear anything theorized that way. Let's try it now.

Twins are both in the same spaceship, having a rope pulling contest. The pulling directions are perpendicular, so that one flattened twin is pulling a contracted rope, while the other twin, who has a small width, is pulling a thin band that is not contracted lengthwise.

(there's a pulley which makes the different pulling directions possible)

So we may guess that the flattened twin is able to pull with quite large force, but just a short distance, while the other twin is weak, but has longer hands which make a longer pulling distance possible.

 

[nitsuj]

In your example, speed is same where as time and distance are different. This is understandable.

But in the twin paradox case, not only is speed different but time, distance( length contraction), mass (increase in mass), KE, age etc. are different. This is a completely bizarre scenario. Everything is different.

This is a great time to learn about invariant measurements.

one of the most fundamental invariant measurements is the order of events. Every observer must agree on the order of events. This is called an invariant causal system/structure.

This is represented by the spacetime interval. This is more Physically fundamental then time/length.

One of the consequences of every observer measuring the same order of events is differential aging. its strange at first to think that your age is not as physically fundamental as causal structure, but age/aging not as important as the sanity of the universe

Makes me wonder if aging could be is a weak emergence

Mass is also invariant.

Also, once you learn more about the temporal/spatial dimensions you will see what a simple easy to understand shockingly accurate analogy the shorter path driven, earlier arrival is.

 

[PeterDonis]

Twins are both in the same spaceship, having a rope pulling contest. The pulling directions are perpendicular, so that one flattened twin is pulling a contracted rope, while the other twin, who has a small width, is pulling a thin band that is not contracted lengthwise.

(there's a pulley which makes the different pulling directions possible)

So both twins are at rest relative to each other, the pulley, and the spaceship? And, in the frame in which all of them are at rest, both twins' ropes are the same length?

So we may guess that the flattened twin is able to pull with quite large force, but just a short distance, while the other twin is weak, but has longer hands which make a longer pulling distance possible.

If my assumptions above are correct, then neither twin will have any mechanical advantage. The fact that in a frame in which the spaceship/pulley/twins are moving, one twin's rope appears shorter, has no effect on the actual mechanics of the rope pulling.

 

[jartsa]

So both twins are at rest relative to each other, the pulley, and the spaceship? And, in the frame in which all of them are at rest, both twins' ropes are the same length?

Yes.

If my assumptions above are correct, then neither twin will have any mechanical advantage. The fact that in a frame in which the spaceship/pulley/twins are moving, one twin's rope appears shorter, has no effect on the actual mechanics of the rope pulling.

Ok.

 

[ghwellsjr]

This is a great time to learn about invariant measurements.

one of the most fundamental invariant measurements is the order of events. Every observer must agree on the order of events. This is called an invariant causal system/structure.

This is represented by the spacetime interval. This is more Physically fundamental then time/length.

One of the consequences of every observer measuring the same order of events is differential aging. its strange at first to think that your age is not as physically fundamental as causal structure, but age/aging not as important as the sanity of the universe

Every observer must agree on the order of events? It seems to me that this could only be true if there were only one frame to consider--unless I'm totally misunderstanding you. Can you please explain?

And can you point to a definition of "invariant causal system/structure"? I never heard of this.

 

[nitsuj]

Every observer must agree on the order of events? It seems to me that this could only be true if there were only one frame to consider--unless I'm totally misunderstanding you. Can you please explain?

And can you point to a definition of "invariant causal system/structure"? I never heard of this.

Ill get a decent reply up, but wiki causal system. essentially the future doesn't effect the past.

A very simple way to picture this is despite differential aging...the incremental nature of aging is always there. Going faster then c breaks this incremental nature. the continuum always "goes" 1-2-3-4-5 and we all agree on that ordering. it never goes 1-3-2-5-4...if that's the case you have gone too fast and ruined the universe for everyone else

Doppler is the most clear example I can think of at this moment, another fun one is if everyone is observing you, we all will agree on the order of the physical occurrences as they happen to you, no matter the comparative motion. however that does mean the observers will (generally) not agree on the simultaneity of events where there is a spacelike separation. I.e. the ordering of your's and mine birthdays. Since we don't celebrate them together there is a spcelike separation between those occurrences, so in some frame it could be I turn older then you, and in another frame you turn older then me.

I really like this way of thinking of it because it precedes the measurements of length/time between the physical occurrences. If someone agrees that we all observe the same order of events/happenings/physical occurrences, it should follow that measures of time/length would be different depending on the comparative motion/speed.

 

[Nugatory]

Every observer must agree on the order of events.

That is not correct. What is correct:

Every observer must agree on the order of time-like separated events.

 

[Dale]

So, what is my correct age/ Can someone measure it be less than 80 years? How?

Your age at a given event along your worldline is the proper time along your worldline from your birth to that event. It is frame invariant, so all reference frames agree on its value.

It helps to think geometrically. If you have a curve in a plane and two points on that curve, then the length of the curve from one point to the other is independent of the coordinate system that you use. Age is the "length" of a massive particle's line in spacetime.

 

[nitsuj]

That is not correct. What is correct:

Actually that's more specific. The correctness depends on "event". Here it is a physical occurrence, an interaction between to previously separated objects (objects = not spacetime).

 

[WannabeNewton]

What you said is only true for two events that lie in the same light cone. To see this, if $t_{1} < t_{2}$ in one frame but $t'_{1} \geq t'_{2}$ in another frame, then $\Delta t'_{12} = \gamma(\Delta t_{12} - v\Delta x_{12})\leq 0$. Now if $\Delta t_{12}\leq 0$ as well then this would be perfectly possible but we know that $\Delta t_{12} > 0$ so $\left | \Delta t_{12} \right | \leq v\left | \Delta x_{12} \right |< \left | \Delta x_{12} \right |$ thus $-\left | \Delta t_{12} \right |^{2} + \left | \Delta x_{12} \right |^{2} > 0$ which is a contradiction if both events lie in the same light cone.

An event that is outside the lightcone of a given event need not obey this. Think of the train and lightning thought experiment: the two events occur simultaneously in one frame but occur at different times in another so the order of the events is not preserved under Lorentz transformations for space-like separated events.

 

[nitsuj]

An event that is outside the lightcone of a given event need not obey this. Think of the train and lightning thought experiment: the two events occur simultaneously in one frame but occur at different times in another so the order of the events is not preserved under Lorentz transformations for space-like separated events.

And what is the physical significance of RoS? non-physical need not obey physical, literally that simple. The lighting strikes are physically independent. So it doesn't matter if me on the train sees both happen at the same time and you on the platform sees them occurring separately, or vice-versa. All that needs to be done is change the angle of perspective through 4D to change that type of spacelike ordering, clearly you or me moving has no impact on the individual lighting strikes.

For ordering, every observer agrees I am in the centre of the train, right in the middle of the "event" that's the front of the train & the "event" that's the rear of the train. There is no (inertial) physical angle of approach through spacetime that can change the fact I am in the middle of the train. The are many angles of approach that can change the simultaneity of the what happens at the front of the train compared to the back of the train, that perspective ignores the causal structure of the whole system (lightning, me , you, train) and focuses just on our comparative coordinating of the spacelike separated lighting strikes.
the causal presentation of c "ignores" what's physically meaningless...i.e. the comparative measures of length/time. What is physically meaningful is the order of the physical occurrence. That's all that matters for comparative observations, not how long it took and the length of the distance.

 

[WannabeNewton]

That simultaneity is not a Lorentz invariant concept; this is unlike Galilean relativity wherein simultaneity is a Galilean invariant concept.

 

[WannabeNewton]

It's weird but the direction of comparative motion (me-train to you-platform) means the first strike is at the front, and the last strike is at the rear for me.

The order of spatial locations is also not preserved under Lorentz transformations if events are not space-like separated. If $x_1 < x_2$ in one frame then I can easily make it so that $x'_1 > x'_2$ in another if the events are e.g. time-like separated.

For $\Delta x_{12} > 0$, $\Delta x'_{12} = \gamma(\Delta x_{12} - v\Delta t_{12}) < 0\Rightarrow \Delta x_{12} < v\Delta t_{12}\Rightarrow -\left | \Delta t_{12} \right |^{2}+\left | \Delta x_{12} \right |^{2} < 0$ so it is perfectly possible for events that are time-like separated. For example if $\Delta t_{12} = 5, \Delta x_{12} = 3$ then the above implies that if I take e.g. $v = \frac{4}{5}$ then $\Delta x'_{12} = \frac{5}{3}(3 - 4) = -\frac{5}{3}$ so the order of spatial locations has reversed for these time-like separated events.

 

[ghwellsjr]

...that does mean the observers will (generally) not agree on the simultaneity of events where there is a spacelike separation. I.e. the ordering of your's and mine birthdays. Since we don't celebrate them together there is a spcelike separation between those occurrences, so in some frame it could be I turn older then you, and in another frame you turn older then me.

This is correct but it sure seems to contradict your statement that "Every observer must agree on the order of events". Do you mean every observer agrees with the order of events along every world line?

I really like this way of thinking of it because it precedes the measurements of length/time between the physical occurrences. If someone agrees that we all observe the same order of events/happenings/physical occurrences, it should follow that measures of time/length would be different depending on the comparative motion/speed.

I don't see your logic. You seem to want to explain relativity without stating it as a principle or a postulate.

 

[nitsuj]

This is correct but it sure seems to contradict your statement that "Every observer must agree on the order of events". Do you mean every observer agrees with the order of events along every world line?I don't see your logic. You seem to want to explain relativity without stating it as a principle or a postulate.

I have to read what world lines are. I imagine it's the same as saying we each have our own proper time. In other words I don't know the strict definition/concept of worldlines well enough to include in a retort/response.

I'd call causal system an axiom...and am not familar enough with "theories" to know it's enough to not have to mention the SR postulates. Intuitively I can't help but feel it does.

That said people much smarter then me have probably covered this train of thought many times. And the SR postulates haven't been replaced by a single axiom.

Regarding your first question, it may answer it wording it this way. The events as they happen to an object is invariant. For aging, this could be said as "the "evolution" of composition is invariant"

 

[ghwellsjr]

I have to read what world lines are.

A worldline is merely the path an object traverses through spacetime.

I imagine it's the same as saying we each have our own proper time.

This is not true for massless objects such as photons which don't have any time associated with them but it is true for massive objects although I don't know why you would focus just on that particular aspect to explain a worldline.

In other words I don't know the strict definition/concept of worldlines well enough to include in a retort/response.

I'm still trying to figure out what you mean by your seemingly contradictory statements. You must at least know what you meant by those statements.

I'd call causal system an axiom...and am not familar enough with "theories" to know it's enough to not have to mention the SR postulates. Intuitively I can't help but feel it does.

I agree that our universe is a causal system, I'm just trying to understand why you think that aspect of the universe has anything to do with why two twins would age differently or why you would say:

One of the consequences of every observer measuring the same order of events is differential aging. its strange at first to think that your age is not as physically fundamental as causal structure, but age/aging not as important as the sanity of the universe

That said people much smarter then me have probably covered this train of thought many times. And the SR postulates haven't been replaced by a single axiom.

You're the first and only person that I have ever heard that expresses that a causal universe provides an explanation for differential aging and I'm still waiting for you to explain that connection.

 

[nitsuj]

I will, but it takes me a long time to think it through and write it out so there is no "holes" in it, I think I may even have to make a definition for aging. (yay wiki defines it pretty well, don't even have to be specific i.e. senescence)

At work right now so in the est. afternoon I can reply much better, and am excited to too..."stupid" work getting in the way of physics musings lol.

About wordlines, Oh, then no not what I meant, we all take different paths through spacetime, which is what leads to the different measures of time/length comparably (less there being no comparative motion). causality is the reason for the interval.

 

[nitsuj]

Surely by now you (wannabeNewton) know I cannot read math. lol

Maybe I need to define a physical occurrence because you(WannabeNewton) keep mentioning separations between objects. A physical occurrence is the moment of interaction between previously separated objects with a “focus” on one of the objects...no concern for the “size” of separation just that there was a separation & that there is a moment when the two objects contact; which could be idealized or actual. This is not about how we measure spacetime and how we plot things differently on our coordinate "charts" if there is relative motion between us. It is strictly about the order of physical occurrences. From a physical perspective anything else is us measuring and plotting on paper i.e. not physical for the objects themselves (less you the observer, measuring tools, yada yada yada)

So there is me in the gym ready for an onslaught of dodge balls to be thrown at me. I'm tough so Ill be sure to be hit by each one. Each one is identified independently...numbered 1 through 10 and thrown at me in an incremental order every minute from 10m away (both measured in my frame). Every observer in the (local) universe will agree on the order the balls hit me. Few will agree on the 10m length & 1 minute time between throwing each ball.

Some will observe little length separation (non zero min.) between me and the ball throwers and a greater then 1 min delay (less then an infinite time path between balls being thrown).

These different observations all see the same order of physical occurrence.

So all that needs to be said is physics (SR) has a causal structure. There are only two mutually exclusive, physically relevant possibilities. The physical occurrence(s) that will occur and the physical occurrence(s) that has (had) occurred. However you measure that separation is up to you and is physically irrelevant. What is not physically irrelevant is the fact there is a separation between the objects. Clearly as we know the length of separation is irrelevant. We could easily make it so the length of separation is less, but that will cause a “delay” for us...which is maintaining the causal structure. Let’s use the dodge ball example.

While I am getting hit by the dodge balls I'm watching you in motion taking observations of the onslaught. Idealize exactly the moment you receive the first lightlike notice of the physical occurrence of ball #5 hitting me, you read your laboratory wrist watch (there cannot be separation between you and clock for this) and it reads 1:00. Note how you receiving the “notice” is it self a physical occurrence. We both agree on that 1:00 o'clock time, despite our independent measure of proper time.
Every observer would agree with that physical occurrence...you receiving notice of ball #5 hitting me when your wrist watch reads 1:00. We can add every observer watching every other observer to note the order each receives the observation of the incremental ball numbering and which order they hit me. All will agree 1-2-3 and on. That's causal ordering. Few will agree on the length/time measures, and that is non-consequential to the physics itself.

But realize that if you are measuring a separation between objects that will never interact (idealized or actual) it is a physically meaningless result/measure, this is actually physically impossible to do but some love diagrams so I mention it idealized. Big deal if you measure a length or a time interval of some sort between objects, sure it's important to you specifically, but the structure of the universe isn't about your measurements of length/time. It's about physical occurrence, and the continuity/order of these physical occurrences, that's it. Even motion is physically meaningless, that’s merely the geometry between physical occurances (who "has" the kinetic energy in comparative motion? Is it even a physical property?) no matter how fast you try to go there will always always always be a length of some measure of 10m or less (but not zero) between me and the dodge-ball ball "throwers" and a time interval of 1min or more (as in longer time path) but less then infinity.

It’s not much of a leap to extend this to differential aging.

In the dodge-ball example, every time the balls hit me I am one minute older; in my frame. In the frames moving compared to the dodge-ball “system” (or would be the case aging of a body) this is happening more slowly than “1 minute older” every time a ball hits me. Let’s say in your frame it’s two minutes between ball throwing/hitting me.

Im going to introduce a magical character named causal system referee. He/she is an observer that makes sure this ordering is maintained. Let’s place this referee far enough away that the field of observation includes the dodge-ball “system” and your frame within a 150 degree or so angle of “view”. This referee is in motion compared to the dodge-ball “system” & you; so that he/she measures one and a half minute time intervals between ball throwing.

This referee will say (as will every other observer) that whether or not you started moving from your position at the moment (any observer’s “moment” of that physical occurrence) ball #5 had hit me you would receive the initial light like notice when your laboratory wrist watch read 1:00, you cannot “speed” away from causal structure. The comparative motion is physically meaningless to the objects themselves.

So for differential aging, the only requirement is causal structure. Regardless of your relative motion, regardless if you measure 1 or 2 minute intervals between ball throwing you get the causal physical occurrence of “notice” when your laboratory wrist watch reads 1:00. For that to happen I must age slower then you from your frame and you must age slower then me from my frame.

So long and short of it is, SR is merely the geometry of physics, not so much physics itself. What’s so intriguing, or what I find so intriguing is that geometry includes a measure of time which leads to geometric “time traveling to another observers future”, equally though it leads to length contracting, not as “exciting” differential aging between twins or what have you.

The only “physics” in SR seems to be “built in” with the mechanical physics postulate. Everything else is geometric “modifiers” to those mechanics. This more or less is saying we live in a continuum, and it’s a causal system.


Trying to reduce it, everything in the (local) universe is in motion. Some are inertial locally by definition, for example my body, a dodge-ball game, the Earth, but that is by definition only. Note we do live in a continuum. So when I say objects assume it’s in motion compared to something else somewhere, we already do but vaguely, here in must be implicit & obvious.

So if everything is in motion, all these things measure length/time between other objects from comparatively different angles across spacetime due to the motion.

So are the simple statements everything is in motion & within a causal structure enough for differential aging. I think so. Ultimately this can be restated as aging (not strictly senescence) is a geometric phenomenon, but the causal structure results in differential aging.

 

[PAllen]

It could be interesting to examine the following:

Both a Galilean universe and an SR universe are causal. However, the the former provides a total ordering of events, while the latter only a partial order (events that have an invariant order are causally connected; those that don't are causally disconnected). Is it possible to come up with a chain of reasoning that leads to differential aging strictly from the causal structure of SR (as distinct from Galilean relativity)? If not, what minimal additional assumption is needed?

I don't have time to think about this in detail now, but I could see a chain of reasoning like: if all world lines between two events have the same clock time, then a global time (and thus time ordering) can be set up, violating the causal structure of SR.

 

[ghwellsjr]

So are the simple statements everything is in motion & within a causal structure enough for differential aging. I think so. Ultimately this can be restated as aging (not strictly senescence) is a geometric phenomenon, but the causal structure results in differential aging.

There's nothing in your post about differential aging in spite of your continual claims.

You are talking about Time Dilation, not differential aging.

Differential aging is when two objects/clocks/observers start out colocated (a physical occurrence, in your terminology) at which point they synchronize their clocks, then they separate and eventually they become colocated again (a second physical occurrence) at which point they compare the accumulated times on their respective clocks and find them to be (possibly) different.

 

[ghwellsjr]

So there is me in the gym ready for an onslaught of dodge balls to be thrown at me. I'm tough so Ill be sure to be hit by each one. Each one is identified independently...numbered 1 through 10 and thrown at me in an incremental order every minute from 10m away (both measured in my frame). Every observer in the (local) universe will agree on the order the balls hit me.
...
We can add every observer watching every other observer to note the order each receives the observation of the incremental ball numbering and which order they hit me. All will agree 1-2-3 and on. That's causal ordering.
...
In the dodge-ball example, every time the balls hit me I am one minute older; in my frame.

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.

Furthermore, as I said in my previous post, you didn't provide any example of differential aging. However, if we allow the balls to be thrown at different speeds, then we can use your example to show differential aging of the balls.

I'm going to change your scenario a little bit so that it can be drawn on a spacetime diagram that will fit on one page, but the principles still apply even for your example. I'm going to show you in blue, the ball thrower in green, and then I'm going to show just two balls, the first in black and the second in red.

As I said in my previous post regarding differential aging, the two balls are colocated with the thrower at the beginning (at the Coordinate Time of 1 nsec and the Coordinate Location of 12 feet) and take different paths to you at the end of the scenario (at the Coordinate Location of 0 feet) and we will look at how the age of each ball progresses as shown by the dots indicating 1 nsec increments of Proper Time.

First we have the situation where both balls are thrown at the same speed of 0.6c:

Now if you count the dots from the lower right corner where the first ball is thrown until the upper left corner where the second ball hits you, you will see that both balls age by 22 nsecs.

In the next post, I will show three more examples where the second ball is thrown at different speeds.

After that, I invite you to explain how "the causal structure results in differential aging", ok?

 

[ghwellsjr]

Now I'm going to show the same scenario except that the second red ball will be thrown at a slower speed, 0.479c:

Count the dots again and you will see that the black ball ages by 27 nsecs while the red ball ages by 28 nsecs.

Next, the red ball is thrown at 0.8c:

The black ball ages by 17 nsecs and the red ball by 15 nsec.

Finally, the red ball is thrown at 0.923c:

The black ball ages by 16 nsecs and the red ball by 12 nsecs.

Note also that the order in which the balls hit you is different than the order in which they were thrown.

Also note in these three cases that the time delta in which the balls hit you is not the same as the time delta in which they were thrown.

So now here is your opportunity to explain how "the causal structure", which is clearly apparent in all these diagrams, "results in differential aging".

 

[nitsuj]

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.

I was going to retort to your previous reply, but you're changing the post around to make a point. I'm not gunna "play".

No George, it's one minute between ball throwing. the spacetime interval is crucial...

My post does explain differential aging from a causal perspective.

 

[nitsuj]

It could be interesting to examine the following:

Both a Galilean universe and an SR universe are causal.

Show me causal structure in a gallian universe. We will end with infinite speed...does causal structure make sense when we can go infinitely fast? What does infinite fast mean?Geometry in a Galilean universe excludes time as a component (of the geometry). It even hand waved away the speed of gravity saying it's instant. Yea that makes physical sense

When time is a component of geometry, causal structure leads to differential aging & an invariant speed.

a Galilean universe is full of logic "holes", SR is Fort Knox lol

 

[ghwellsjr]

I was going to retort to your previous reply, but you're changing the post around to make a point. I'm not gunna "play".

I didn't change anything that you specified. And I'm trying to help you make your point.

No George, it's one minute between ball throwing. the spacetime interval is crucial...

Then will you agree that my first diagram in post #35 is similar enough to your scenario that you can make your point with it?

And I thought you said you "cannot read math". How do you determine the spacetime interval in your scenario without math? What is its value and what are the two events that you are calculating it between? And if it's so crucial, why didn't you mention it in your very long post?

My post does explain differential aging from a causal perspective.

Where do you mention any differential aging?

 

[nitsuj]

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.


After that, I invite you to explain how "the causal structure results in differential aging", ok?

The order the balls hit me as I see it, will be the same order every observer sees the balls hit me. No speed can have it such that ball 5 hits before ball 4. For your charting, this is very clear. If there is no separation between me and the ball there is no way to separate it so ball 5 can "get in there" and hit me before ball 4.

This is NOT about the order they seen traveling, it's the order they hit me The order they leave the Single ball throwers hands will also be invariant, what is not invariant is how they are seen traversing spacetime, which is to your point.

I have explained it, you "distort" the meaning, perhaps unintentionally, but none the less spoils any attempt to discuss it

 

[ghwellsjr]

The order the balls hit me as I see it, will be the same order every observer sees the balls hit me.

You are spending a lot of time "making a point" that everyone already agrees with. Yes, whatever order the balls actually hit you is the order you see them hit you and the order that everyone else sees them hit you. I made no comment about this issue. I only showed one frame, your rest frame. I was not and am not concerned with what other frames or observers might see. This issue has absolutely nothing to do with differential aging. If you would show me the two objects/clocks/observers that you are considering to have aged differently, then I can show you how all frames and observers will agree on their differential aging if you want. But you haven't made any comment about this even though I keep asking you to do so.

No speed can have it such that ball 5 hits before ball 4.

I agree, no speed that is applied exactly to every ball will result in them hitting you in a different order. I already stated this fact.

For your charting, this is very clear. If there is no separation between me and the ball there is no way to separate it so ball 5 can "get in there" and hit me before ball 4.

This is NOT about the order they seen traveling, it's the order they hit me The order they leave the Single ball throwers hands will also be invariant, what is not invariant is how they are seen traversing spacetime, which is to your point.

No, that's not my point. I didn't show any scenario transformed between two different frames. All my diagrams were for the same frame, just different scenarios.

I have explained it, you "distort" the meaning, perhaps unintentionally, but none the less spoils any attempt to discuss it

You aren't discussing the issue you claim to be discussing. That's the problem. You think there is some differential aging going on in your scenario but there isn't. If you think there is, please point it out.

 

[Nugatory]

Justin, back in #29 you say

I have to read what world lines are. I imagine it's the same as saying we each have our own proper time. In other words I don't know the strict definition/concept of worldlines well enough to include in a retort/response.

It's really hard to communicate effectively about causality and time without this understanding. Watching you try makes me feel as if I'm watching someone using Roman numerals to explain long division - the representation is getting in the way.

 

[nitsuj]

Justin, back in #29 you sayIt's really hard to communicate effectively about causality and time without this understanding. Watching you try makes me feel as if I'm watching someone using Roman numerals to explain long division - the representation is getting in the way.

I appreciate that with respect to disusing spacetime between objects. Causality is about the objects themselves and observations of them.

I don't need to draw diagrams representing spacetime, for this point. George says we all already agree on causality.

All that I need to do is assume a "global/local/whatever" causality, which isn't at all about spacetime. And either is differential aging, it's about the objects themselves and how physical occurrences "play out" and how we all agree on the order. If it's conceptually necessary, then include the c postulate (speed limit).

 

[WannabeNewton]

Well for starters, causality is all about causal curves so it involves exactly what Nugatory mentioned, and George's point is that differential aging simply deals with the different integrated proper times along two different space-time "trajectories" that have the same initial and terminal points (I put trajectories in quotes because technically nothing moves in space-time so it's not like we're tracing out a curve following the path of a particle in the Newtonian sense of a trajectory) and what you are saying is not related; I'm not sure you understand what causal structure is (and by the way, Galilean space-time is a known construction so what you said in post #38 is incorrect).

 

[nitsuj]

If you think there is, please point it out.

It is there. I'll try to think of a better way to structure what I wrote so the logic is more apparent.

Like I PM'd you, this is really just making a clear distinction between geometry & physical occurrence.

My perspective is you keep discussing spacetime and making diagrams, which isn't at all what this is about. It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

 

[nitsuj]

Well for starters, causality is all about causal curves

(and by the way, Galilean space-time is a known construction so what you said in post #38 is incorrect).

Yea, I can't make anything of that.

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

 

[WannabeNewton]

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

At a basic level:
http://ls.poly.edu/~jbain/spacetime/lectures/11.Spacetime.pdf
http://faculty.arts.ubc.ca/ssavitt/Courses/Phil462B/Galilean%20Spacetime.pdf

At a more advanced level: http://arxiv.org/pdf/gr-qc/0211030v2.pdf

 

[PAllen]

Show me causal structure in a gallian universe. We will end with infinite speed...does causal structure make sense when we can go infinitely fast? What does infinite fast mean?Geometry in a Galilean universe excludes time as a component (of the geometry). It even hand waved away the speed of gravity saying it's instant. Yea that makes physical sense

When time is a component of geometry, causal structure leads to differential aging & an invariant speed.

a Galilean universe is full of logic "holes", SR is Fort Knox lol

Completely wrong on all counts. Galilean relativity is simply the c->∞ limit of SR. It is true that there is no (non-degenerate) spacetime metric, but that is the point - space and time are separable. The causal structure is stronger than SR because all pairs events have invariant (under Galilean transforms) causal order. Thus, both theories have causal structure, but not the same one. Obviously SR matches reality, but that is not relevant.

In case you didn't notice, I was wondering whether there is some validity to what you are arguing: Is the specific causal structure of SR versus Galilean relativity (alone) sufficient to require differential aging? I think the answer is probably yes, with maybe a few technical assumptions required, but I haven't put together a rigorous argument for this.

 

[ghwellsjr]

You aren't discussing the issue you claim to be discussing. That's the problem. You think there is some differential aging going on in your scenario but there isn't. If you think there is, please point it out. [Quote expanded to include context.]

It is there. I'll try to think of a better way to structure what I wrote so the logic is more apparent.

It's not a matter of logic, it's simply a matter of stating which two objects/observers/clocks are the ones engaged in differential aging. I already pointed out what you could have answered:

Consider any two of the ten balls. They start out colocated with the thrower. One of them leaves and goes (is thrown) to you. Some time later, the second ball leaves (is thrown) and goes to you at which point those two balls are again colocated. Now we can calculate (if we know their speeds) the amount of aging each ball achieved from the time they were together, then separated, then rejoined.

But you rejected my suggestion, insisting that somewhere else in your scenario is another example of differential aging. I'm just asking where. You don't have to explain how we determine their respective aging, just who (or what) they are.

Like I PM'd you, this is really just making a clear distinction between geometry & physical occurrence.

If you are saying that you have not yet gotten to the differential aging part, then I agree. However, you're going to have to start all over again with a different scenario if you want to demonstrate differential aging in your discussion.

My perspective is you keep discussing spacetime and making diagrams, which isn't at all what this is about.

I'm not the only one discussing spacetime (as if there's something wrong with that):

No George, it's one minute between ball throwing. the spacetime interval is crucial...

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

If you don't like my diagrams, then just ignore them, I thought they would help you in your explanation.

It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

Ok, I will wait for you to present the "next step". I had no idea your long post was not intended to be an explanation of how "causal structure results in differential aging".

 

[nitsuj]

Completely wrong on all counts. Galilean relativity is simply the c->∞ limit of SR. It is true that there is no (non-degenerate) spacetime metric, but that is the point - space and time are separable. The causal structure is stronger than SR because all pairs events have invariant (under Galilean transforms) causal order. Thus, both theories have causal structure, but not the same one. Obviously SR matches reality, but that is not relevant.

In case you didn't notice, I was wondering whether there is some validity to what you are arguing: Is the specific causal structure of SR versus Galilean relativity (alone) sufficient to require differential aging? I think the answer is probably yes, with maybe a few technical assumptions required, but I haven't put together a rigorous argument for this.

The reality point I suppose could be a matter of opinion. The causal structure is NOT stronger...because it doesn't even exist. It's non sense to compare impossible things to reality and pose it as a point.

Again show me causal structure in that "metric" of infinite speed. I'll just go faster.

In case you didn't notice, you said I was wrong on all counts, that contrasts your agreement with how I described the "metric" as not including time. & the lack of a speed limit. Which are the only two points I mentioned in retort.

This is to your point of SR "breaking" causal connection (spacelike), it has too less the non sense of infinite speed.

If you really feel there is a true & meaningful "causal" structure in Galilean geometry you won't ever agree with what I am saying, if you laugh at that proposed structure as physical non sense then you may see where I am "coming from" with my perspective.

And I hope I don't come across as arguing, if it does I don't want to continue...it's not at all how I wish to "present" a perspective.