Question Relativity and the past and future

[swansont]

That makes sense. If the earth is spinning (rotating), and a clock is left on the earth relative to one in a plane, then you must account for the fact that the clock left on earth (not brought on the plane) was spinning (rotating) with the earth.

 

Also, thanks for the clarification above. When I typed my post, I was doing it from memory and thought that one clock was on the plane and one clock was on the ground, but saw the reference to four clocks in the wiki link so adjusted my words.

 

So, with the currently even more accurate clocks, my guess is that they can confirm the predictions on even shorter flights (aka... not complete circumnavigation of the globe).

 

 

We send a van to do remote satellite calibrations elsewhere in the US, which then returns and you check the local linkup to "close the loop" and make sure no errors have been introduced. I was reading a trip report and noticed that the accumulated kinematic time dilation from driving at <70 mph for a cross-country trip & return was of order 1 - 2 ns, and you can measure that with the clocks compared to the main ensemble that comprises the "master clock."

 

People often say that the effects of relativity are only noticed when you go close to the speed of light, but it's also the case that they are noticed when you have very good clocks. We're almost to the point where putting the clock on the second floor vs the first floor will give a measurable difference in performance, and another step away from when solid-earth tides, which are ~half a meter, will become noticable (gravitational dilation is a part in 10^16 per meter)

 

What is the essence of "inertial frame" here? I find confusions. It seems we are saying that rotation of the planet is an upset of that. By themselves, velocities are relative, so I think this is a subtle and cool point. It relates to my previous question.

 

Since the surface is rotating it's accelerating and thus not inertial. You have to use an observer, e.g. sitting above the north pole (which is what is used in the paper) in order to do the analysis.

 

You can (and people do) use an earth-centered inertial (ECI) frame, but that introduces extra terms, much like a rotating coordinate system has pseudoforces to make thing behave in a Newtonian fashion. In the ECI you have the Sagnac effect, which introduces a time difference for travel parallel to the equator. Something like 207 ns is introduced for a complete circumnavigation in the ECI frame.

[hmmrn]

It's hard to explain why they're not the same age better than people have done in this thread to be honest. You have to stop thinking of time as an absolute as you do with distance or mass. There's no way to acctually "meassure" time as we do on earth using clocks and such.

[asprung]

How can one man be living in the year 2000 and another in the year 3000 and yet share the same "PRESENT"?

 

How can one man be living in the year 2000 and another in the year 3000 and yet share the same "PRESENT"?

[Norman Albers]

You have done this for quite a few years, asprung. I still have to lay this out in detail in order to see it. You can do the 'infinitely long trains' or the 'police car with a very long set of lighted antlers'. Let's say that we sitting in Earth have established, by radio communication, a chain of posts on the Moon and on Mars, whatever, and that we synchronize clocks. This means that we correct for large time delays in propagation, right? A moving spaceship blows by us at significant speed and we agree on our clocks at that moment (we can do this at any one spacetime point). What shows on the spaceship clock as it whizzes close by our observer on the moon? Furthermore, if they "pull a fast 180", that great term from STARTREK, what happens coming back? At first you can drive yourself nuts saying, "how can there be a choice of which gets older when the situation looks symmetric?" The klinker lies in the disagreements in simultaneous time. This has been established in our Earth frame but it is not so as observed by the ship.

[iNow]

How can one man be living in the year 2000 and another in the year 3000 and yet share the same "PRESENT"?

 

Why do you think that one is living in the year 2000 and why do you think the other is living in the year 3000? If they share the same present, they are living in the same year.

 

 

Addendum: If one brother was in the year 3000, then the other would surely have died by then, and they would not be able to share the same "present."

[hmmrn]

Everyone lives in the same year no matter what they choose to call it, because the only time that really exist is now. A calendar is something humans have invented to keep track of "time".

[Norman Albers]

Yet states evolve.

[Janus]

How can one man be living in the year 2000 and another in the year 3000 and yet share the same "PRESENT"?

 

How can one man be living in the year 2000 and another in the year 3000 and yet share the same "PRESENT"?

 

 

Because one is "Earth time" and the other is "Ship time" and the year 2000 "ship time" is the same as the year 3000 "Earth time", they are the same "moment" when the two meet up.

 

The twin in the spaceship simply ages slower and flips his calendar slower than his Earth counterpart. Thus when he returns to Earth in the year 3000 "Earth time", he will have experienced less time as having passed, but he will still return to Earth in the year 3000 according to Earth calendars.

 

The two twins will disagree as to how much time has elasped between the moment they parted and the moment they re-united, but nothing keeps them from re-uniting.

[asprung]

According to special relativity it would appear that a space twin’s time and ageing could pass slower than his earth brother while they both shared the same present (now). How could this be?

[iNow]

Let's start here. Do you understand that the space twin experiences his own time normally, and the earth twin experiences his own time normally also?

 

 

Do you understand that it's only relative to his earth brother that the space twin's time passes "slower?"

[thedarkshade]

Yes that is correct. Not only for them, but for everything. According to the theory of relativity nothing experiences the same time. You and me don't experience the same time. That's time dilation. I know it violates the common sense, but hey, saying the sun has 1 million times the volume of earth violated ancient men's common sense too.

 

People experience different times because they travel at different velocities (or don't travel at all), and experiencing times depends at velocity. How can it be? I know it sounds bizarre. Here is the formula that exactly tell how much time you experience less while you're traveling than those who are not. I like to call it the Einstein Factor.

 

[math]f=\sqrt{1 - \beta^2}[/math] where beta is called light speed (v/c)

 

Suppose you are traveling at 90% speed of light. Then [math]\beta=0.9[/math]. You plug that into equation and you exactly find how much less time you are experiencing.

 

[math]f=\sqrt{1 - \beta^2}=\sqrt{1 - (0.9)^2}=\sqrt{ 1 - 0.81}[/math]

[math]f=\sqrt{0.19}=0.435889894354067355 and so on[/math]

 

And by Lorentz factor you get:

 

[math]\gamma=\frac{1}{\sqrt{1 - \beta^2}}[/math]

 

[math]\gamma=\frac{1}{0.435889894354067355}[/math]

 

[math]\gamma=2.294157388...[/math]

 

So your time slows down by a factor of 2.294157388. That means that if your has experienced 2.29 years, you have actually experienced only 1 year, because of the velocity you are traveling with. But that's not just it.

While you traveling, your length contracts (Lorentz contraction). Suppose your rest length is 2m, and at the velocity you are traveling it will change. Let you rest length be [math]l_0[/math] and you contracted length be [math]l[/math]. The equation for measuring how much you contracted looks like this:

 

[math]l=l_0\times \sqrt{1 - \beta^2}=2 \times 0.435889894354067355[/math]

[math]l=0.871779...m[/math],

so now you are that long. But again this is not it. You mass also increases. If your rest mass is 70kg, then your mass while traveling will be:

 

[math]m=\frac{m_0}{\sqrt{1 - \beta^2}}=\frac{70}{0.435889894354067355}[/math]

 

[math]m=160.5910kg[/math]. And the amazing thing is yet to come. Today while I was doing this, I managed to get something. Watch:

 

[math]\frac{m}{m_0}=\gamma[/math]

 

and

 

[math]\frac{l}{l_0}=f[/math] ... now let's test that.

 

 

[math]\frac{m}{m_0}=\frac{160.5910}{70}=2.2941...[/math] see! Just like gamma that we found a bit earlier

 

and

 

[math]\frac{l}{l_0}=\frac{0.871779}{2}=0.4358895...[/math] just like the Einstein factor (i like calling it that way) that we found earlier.

This is the beauty of relativity.

 

So there are three things that happen to an object while he is traveling:

1. Time down

2. Its length contracts

3. Its mass increases

 

But in our everyday lives these are very very small number and that's why we don't notice them

 

 

Cheers,

Shade

[losfomot]

According to special relativity it would appear that a space twin’s time and ageing could pass slower than his earth brother while they both shared the same present (now). How could this be?

 

They can't really both share the same present (now) until the space twin has come home and is in the same reference frame as his Earth brother. Let's say the space twin leaves Earth on his journey in the year 2001... he speeds off at close to light speed... flies around the nearest star (proxima centauri) and comes back to Earth. Once he is back on Earth, the Earth brother will say

 

"It's good to see you, you've been gone for ten years!"

 

To which the space brother will say

 

"What do you mean, ten years? I've only been gone for 2 years!"

 

The year is now 2011 on Earth, and the Earth twin is 10 years older. But only 2 years had passed for the space twin in his spaceship... so he is now (biologically) 8 years younger than his twin brother. But it is still 2011 for the space twin simply because he must conform to Earth's calendar now that he is back... It would be awful hard for him to convince everyone on Earth that, according to his spaceship calendar, it is only 2003 and they should all change their calendars to conform with his.

 

What the twins have just experienced is something called 'time dilation'.

 

As to why this happens... well there could always be an infinite number of 'why's. If I told you it was 'a prediction of relativity', you could ask me why is it a prediction of relativity? Then I would say it was 'a side effect of the fact (postulate) that light travels at the same speed © regardless of the motion of the light source.' You could ask me why does light act that way? Then I would probably say 'I don't know, that just seems to be the way it is'

 

Now if you start asking more specific questions regarding the answers that myself and others have already given you, you might start understanding better...

 

For example... you might ask "Why is 'time dilation' a side effect of the fact that the speed of light is constant in all frames?"

 

Well, when you think intuitively about distance and speed, you can add things up easy peasy. For example If you drive North at 100 km/hr, and your friend is drives in the opposite direction (South) at 100 km/hr, you can figure out how fast you are going relative to your friend by just adding the speeds... 100 + 100 = 200 km/hr.

 

But say you are in a spaceship and you pass your friend at 99% of c. Just after you pass him, he flashes a light after you. How fast is that light beam traveling after you? Intuitively you would think: 'Well, light travels at 100% of c and I am traveling at 99% of c, so the light must be moving toward me at 1% of c' But remember that light travels at 100% of c in all frames. So the light is approaching you at 100% of c.

 

Now, if you think about this, you would conclude that this is impossible... How can the light leave your friend at 100% of c, you are moving away from your friend at 99% of c, and yet the light beam is still approaching you at 100% of c?

 

The only way for this to be true is if your time is passing slower than your friend's time. Think about it... if your time was slowed down (relative to your friend's time) by about 99%, then the light beam's speed would, intuitively, be 100% of c relative to you.

 

(Please do not put any faith in my actual numbers... Your time would not be slowed down by 99% relative to your friend. It would be less than that because time dilation is not the only effect that is taking place (and I think 99% would be wrong even if it were). The actual formula is a bit more complicated than simple addition, I am just trying to show you conceptually so I used 99%. Thedarkshade just gave you the proper formulas if you want to work it out, or there are many websites that will do it for you.. here's one http://www32.brinkster.com/snefru/space/srcalc/srcalc.htm )

[Norman Albers]

You cannot define 'NOW' at different space coordinates to both observers.

[thedarkshade]

You cannot define 'NOW' at different space coordinates to both observers.

Yup! And that's because there is no universal clock. At least not an exact accurate one!

[Norman Albers]

Imagine the spaceship has a sister ship at a moon's distance behind, moving at the same velocity, so that both pass our observation points, here and on the Moon, at what to us is the same moment as per our synchrony. Now the "travelling" pair are free to establish their own synchrony of clocks, adjusting for time delays of L/c. They will not read the same clock times on their two clocks and vice versa. We agree there are two describable events, spacetime points, where we "pass closely", but if the crews did not work as hard as we to understand relativity, they will be upset. One man's space is another man's time. (I feel a song coming on.)

[swansont]

Yup! And that's because there is no universal clock. At least not an exact accurate one!

 

 

Doesn't matter; there is no preferred frame. The difference between frames is not due to any clock's imperfection.

[Norman Albers]

Right on, Swansont. This is major, depending upon the ratio of the speed of light or [math]\beta[/math] at which the frames move. Similarly, in General Relativity, nearing an event horizon severly slows physics in that frame as measured from outside. We witness asymptotic approach, really, and redshift all the way to zero, except upon appeal to quantum physics.

[iNow]

asprung,

 

As you can see, this is not an "intuitive" subject, but there are a lot of people here who want to help you understand. When we help you with your questions, it helps us to answer some of our own, so don't hesitate to ask more.

 

Just... take a deep breath, and read through this thread again. Then, maybe you will understand more than you did when you first asked your question.

[Norman Albers]

Nice attitude. I computed relativistic kinematics as part of an accelerator research team (Princeton, at Brookhaven) in 1970. Two years later I completed a Master's at Stanford, looking at plasmas. Over the intervening decades as a piano tuner and tech, I have read and contemplated. Every time we pass again through the challenging stuff, we GET IT a little deeper. I'm on pass #8 or 9 with quantum theory.

[5614]

Yup! And that's because there is no universal clock. At least not an exact accurate one![/quote']Doesn't matter; there is no preferred frame. The difference between frames is not due to any clock's imperfection.

Indeed. In a thought experiment, which are always nice with relativity, you could easily assume a "perfect" clock.

 

But the whole point with relativity is that there is no preferred or "real" or "The" referrence frame. All frames are equally valid, and as different frames can measure different times (and each time is also equally valid) there is no "real" or universal time - it all depends on what frame you are in.

[Slinkey]

If the twins end up at the same point why are they not the same age?

 

Because one has been acted on by a force and the other has not.

[Royston]

Because one has been acted on by a force and the other has not.

 

That doesn't answer the question...the short answer is, there's no such thing as Newtonian absolute time.

[Norman Albers]

I think it is part of the answer that one has experienced acceleration and the other has not, because that is what distinguishes the two upon return. On the other hand, one can think in terms of the two simultaneous (Earth-Moon) clocks, just asking what the ship's clock reads as it goes by the Moon post. It should read slower, right? The simultaneity of frames is not shared.

[Slinkey]

I think it is part of the answer that one has experienced acceleration and the other has not, because that is what distinguishes the two upon return. On the other hand, one can think in terms of the two simultaneous (Earth-Moon) clocks, just asking what the ship's clock reads as it goes by the Moon post. It should read slower, right? The simultaneity of frames is not shared.

 

If two bodies are floating in flat space time and are not moving relative to one another they do not share the same time frame. They are separated by space however and can list the order of events in differently to each other, more so if they are very far apart. However, should they look at each others clocks they would be ticking at the same rate albeit probably different times.

 

This is because there are no forces acting upon them. The only difference here is the time it takes light to travel between them.

 

Should one start to accelerate away from the other... the situation changes. The one that is accelerating is being acted upon by a force. Should they look at each other's clocks now they would see they are slower than their own.

[Norman Albers]

Can't distant non-moving points define common clock time? You subtract knowing the speed of light and your separation. Or you can imagine a common source clock halfway between. I don't see what you're laying out, Slinkey.