question about reference frames & time dilation

[gib65]

Whenever Einstein's theory of relativity is explained, it always starts out with the premise that the laws of physics are the same no matter what frame of reference you observe them in. How does this idea lead to the dilation of time?

[abskebabs]

Whenever Einstein's theory of relativity is explained, it always starts out with the premise that the laws of physics are the same no matter what frame of reference you observe them in. How does this idea lead to the dilation of time?

There needs to be a slight change to your statement. Einstein's special theory of relativity begins with the assertion that physics is the same in all INERTIAL frames, and following from this the speed of light needs to be the same in all inertial frames of reference. Before progressing it is important to truly understand what an inertial frame is and how it can be defined. I find thinking about subtleties like this really helps avoid confusion later on.

 

It is basically a resolution of the "conflict" that occurs from Maxwell's electrodynamics where a constant is predicted from the equations; this was later found to be the speed of light, but what puzzled physicists was that this velocity did not have attached to it any particular frame of reference.

 

When we take the physical principles that the speed of light is the same in all inertial frames(and so effectively is a law of physics), as well as the fact that physics is the same in all inertial reference frames; it leads us to other implications. For example this leads us to banish the notion of absolute velocity and rest frame, a notion that was actually entertained by physcists a few years before Einstein, who thought the speed of light could be measured with respect to an "ether."

 

How all this leads to time dilation is a good question. The only sufficient answer I feel I can give is that once we start applying these notions to simple situations or thought experiments involving mechanics, we obtain resultant implications such as time dilation and length contraction. Beyond all this though we start to observe connections between space components between events and time components, that in essence reveal what could be called a an underlying spacetime geometry. This is referred to as Minowski spacetime geometry.

 

Note that I have only talked about special relativity so far and not general relativity as I do not have any real knowledge of the latter yet. I may leave this to be handled by someone with a greater knowledge of physics than me. If you would like me to explain how the implications od special relativity are drawn in more detail, using physical examples then please tell me and I will be happy to attempt to. I think that is the great beauty about relativity actually, you just need to have a little imagination and apply these postulates to mechanical situations and the consequences of relativity emerge:cool: .

[gib65]

and following from this the speed of light needs to be the same in all inertial frames of reference.

 

This is the key point I was wondering about. They always start out with the premise that the laws of physics are the same in all inertial frames, but they only get to the particular, and somewhat esoteric, law of light later on. In other words, they try to wow you with the obvious stuff, but leave out one important detail that novices rarely know. Nothing of relativity follows without this crucial detail.

[swansont]

This is the key point I was wondering about. They always start out with the premise that the laws of physics are the same in all inertial frames, but they only get to the particular, and somewhat esoteric, law of light later on. In other words, they try to wow you with the obvious stuff, but leave out one important detail that novices rarely know. Nothing of relativity follows without this crucial detail.

 

Those are the two postulates of special relativity. I'm not sure who "they" are that are omitting the second postulate; it appears in all the treatments of SR that I recall reading.

[lakmilis]

Well, because when you state these inertial frames, one can start messing around with the emerging relative things like was pointed out. Time dilation happens to he who observes, not he who is hmmm, undergoing it.

 

The most common example of time dilation is the bloke in a spaceship with a flashlight. He sits in this flying box which is transparent and sends a beam of light from the flashlight between his legs up to the ceiling of the box with a mirror. distance is D, so in some time t, the light will travel 2D.

 

for him no matter how much faster this box flies along, t remains 2D/c.

 

Now, we all are sitting on a nice field watching the flying transparent box which we imagine flies like a mofo along the sky. As the bloke in the box sends a beam of light upwards, it also for us, has a horizontal displacement. So by the time the light has reached the mirror in the top, for us the light has travelled diagonally with respect to a starting point outside the ship. if the box moves a distance 2L along our lovely sky then time would be [MATH] 2*sqrt(D^2 + L^2)/c > 2D/c [/MATH]

 

Thus, less time passes by for the guy in the box with respect to our frame!!! for him time is still invariantly passing by at his 'local rate'. Like you know, the twin flying very fast to alpha centauri n back will locally be less aged with respect to us on earth. If you already know such examples and is not what you are asking about, I am sorry, it might be useful for others perhaps which look for an easy example of the dilation principle..

 

[ajb]

Time dilation and length contraction can easily be seen by considering the invariant space-time interval [math]\Delta s^{2} = -\Delta t^{2} + \Delta x^{2} + \Delta y^{2} + \Delta z^{2} [/math].

 

Basically this defines a distance of a path in space-time. Consider two different paths in space-time such that the invariant space-time intervals agree. This means they have travelled the same distance in space-time, but not necessarily the same distance in space or time! Only the overall distance in space-time agrees. This is in essence time dilation and length contraction.

[lakmilis]

hmm ajb, it does not state that exhaustively though does it. Can i not find two different sets of values of (x,y,z,t) which yield the same result (for s) and would merely imply different velocities (as you are stating w.r.t. to a given frame) yielding a different time value, for the given displacement in space?

 

say (x,y,z,t) = (0,0,0,0) and (1,1,1,root(3)) ?

[gib65]

Those are the two postulates of special relativity. I'm not sure who "they" are that are omitting the second postulate; it appears in all the treatments of SR that I recall reading.

 

In all the full treatments, I'm sure. To name one person, there's Richard Wolfson of Middlebury College who, in an introductory lecture on Relativity, says that all the bizaar and non-intuitive phenomena that SR predicts follows just from the fact that the laws of physics are the same in all inertial frames. He mentions nothing of the constant speed of light.

[abskebabs]

This is the key point I was wondering about. They always start out with the premise that the laws of physics are the same in all inertial frames, but they only get to the particular, and somewhat esoteric, law of light later on. In other words, they try to wow you with the obvious stuff, but leave out one important detail that novices rarely know. Nothing of relativity follows without this crucial detail.

 

The idea of the speed of light being the same in all inertial frames may seem esoteric at first, but I would urge you try and think deeply about how things would be if this was not the case. For example, whenever we learn Mechanics we always learn abut velocities being measured relative to something else, and there being no meaning to the idea of an absolute velocity. Relativity is basically a revison of this taking into account the predictions of Mazwell's Electrodynamics.

 

In this sense you are absolutely right, there would be no logical reason to start relativity withoutthe result from maxwell's electrodynamics that predicts a speed for EM waves and light, but neglects to mention a frame with which it was measured. It was then conjectured by many physicists that there was an absloute fram with which the speed f light was measured. Experimentally it was later shown such a frame was shown not to exist. Meanwhile, Einstein who was thinking in a rather original way when approaching the problem, was willing to throw away the idea of absolute reference frames which were meerly hopeful conjectures and try to reanalyse mechanics with a different view: That the speed of light was the same in all inertial reference frames.

 

I think it is important to realise how drastically different and original this postulate was in reference to resolving the conceptual difficulties between electrodynamics and Mechanics. But then again when you look at it again, isn't the 2nd postulate just a reaffirmation of the 1st? If there were such an absolute frame with which the speed of light , wouldn't it effectively be a preferential "ether" frame in which the laws of Mechanics including those regarding the 1st law of Newton's mechanics be contradicted, and wouldn't we effectively burying our 1st postulate that physics is the same in all inertial frames if the speed of light could only be measured correctly with respect to one of them?

 

Think about this, and you may come to realise why the 1st and 2nd postulate of relativity go hand in hand, after interpreting the message found in electrodynamics that EM waves propogate at a constant speed, that is worked out without any reference.

 

I think Richard Wolfson isn't wrong in what he has said, he just has neglected to mention to an audience of whom I assume are novices; the subtleties involved in interpreting the laws and equations of electrodynamics. Without an implicit understanding of this you cannot begin relativity.

[gib65]

I think Richard Wolfson isn't wrong in what he has said, he just has neglected to mention to an audience of whom I assume are novices

 

Yes, I agree with this. SR does follow from the premise of inertial frames alone since the absolute speed of light is a law of nature - you just have to know this.

[Farsight]

What most people don't realise is that Einstein buried one of the postulates of SR with GR. Look:

 

"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)." Albert Einstein (The General Theory of Relativity: Chapter 22 - A Few Inferences from the General Principle of Relativity)

 

You have to read what he said. Einstein actually said the velocity of the propagation of light varies. He didn't mean spacetime is curved. Einstein didn't talk about curved spacetime. He wasn't treating velocity as a vector quantity where the speed remains the same but the direction changes. He really did mean that the speed of light changes. But this has been lost in the wash, and people are told they have to accept the constancy of the speed of light as a "law". There's no logic to this. Not when Einstein thought different.

[Klaynos]

Not when Einstein thought different.

 

Science moves forward, Einstein said alot of things we now know to be true.

 

But I believe that when considering GR there is no requirement for c to be constant. But here we are discussing SR, which does.

[Farsight]

SR is subsumed by GR, Klaynos.

 

But nevertheless, time dilation in SR occurs for the same reason as in GR. There's a "scale change" variation in c that you cannot measure locally. You always measure c to be 299,792,458 metres per second, because light defines your time. When you come back from a relativistic round trip and you've only aged one year while I've aged seven, it's because your speed of light was less than mine, even though we both measured it at 299,792,458 metres per second. Your seconds were different, because your c was different, even though you measured it to be the same.

 

I am right about this. This is the real deal. Einstein was right. And that "law" is a veil of ignorance.

[swansont]

Repeating this does not make it correct. What experiment can be done that would confirm this? What implications does it have that could potentially disprove it?

[Farsight]

Pound-Rebka, Shapiro, even GPS. The issue is interpretational, not experimental. This hidden "scale change" variation in c is what "curved spacetime" actually is. You might find that difficult to accept. but ask yourself this:

 

What is curved spacetime?

 

Try explaining it to your grandmother. And remember this: I agree with Einstein.

[Klaynos]

The issue is interpretational, not experimental

 

So what you're saying is it's not science?

[Farsight]

Huh? Of course it's science. The best science you'll see on this forum. Real science. Here's how it works. Let's look at GPS:

 

http://en.wikipedia.org/wiki/Global_Positioning_System

 

According to the theory of relativity, due to their constant movement and height relative to the Earth-centered inertial reference frame, the clocks on the satellites are affected by their speed (special relativity) as well as their gravitational potential (general relativity). For the GPS satellites, general relativity predicts that the atomic clocks at GPS orbital altitudes will tick more rapidly, by about 45,900 nanoseconds (ns) per day, because they are in a weaker gravitational field than atomic clocks on Earth's surface. Special relativity predicts that atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by about 7,200 ns per day. When combined, the discrepancy is 38 microseconds per day; a difference of 4.465 parts in 1010. To account for this, the frequency standard onboard each satellite is given a rate offset prior to launch, making it run slightly slower than the desired frequency on Earth; specifically, at 10.22999999543 MHz instead of 10.23 MHz.

 

The time "runs" a little slower down here on earth, so the GPS satellite clocks are set to run a little slower than normal. It isn't much, but it's real. So you can get a metre ruler, and measure how long it takes for a beam of light to get from one side to the other. You get the same result in seconds wherever you do it, be it on the surface of the earth or in orbit. But that "same result" down here on earth is different to the value you'd get in orbit by 4.465 parts in 1010.

 

We could do something similar if you were travelling at a relativistic speed compared to me. Remember that length contraction only applies to the direction of travel, so we hold our rulers in a transverse fashion. It's the same size metre, but the seconds are different, so c is different too. In General Relativity the length contraction is radial, akin to the direction of motion in Special Relativity.

 

Wherever there's time dilation, it's because c is different. You can't measure it to be different, because the speed of light defines how you count time. It's a "scale change", and we're totally immersed in it. People call this "curved spacetime" without actually understanding what "curved spacetime" is.

 

It's just all so incredibly simple. Once you see it you'll be amazed that other people can't.

[Klaynos]

Now if my relativity is correct, if you where to hold a meter stick transverse to the direction of motion, and then measure this stick in a moving frame relative to the stick then that measurement would show you that it is not transverse but at some angle?

[swansont]

And now we get back to the effects that depend on c vs the ones that depend on c^2. Why do nuclear reactors work under condition where c should be different?

[Farsight]

Because it's a total scale change. It affects everything because everything is in essence made out of light - as demonstrated by pair production, wherein a gamma photon is transformed into an electron and a positron.

[Klaynos]

Because it's a total scale change. It affects everything because everything is in essence made out of light - as demonstrated by pair production, wherein a gamma photon is transformed into an electron and a positron.

 

Doesn't that mean light is made out of electron positron pairs?

[lakmilis]

Now if my relativity is correct, if you where to hold a meter stick transverse to the direction of motion, and then measure this stick in a moving frame relative to the stick then that measurement would show you that it is not transverse but at some angle?

 

Nope, it could appear so to observers though

[Klaynos]

Nope, it could appear so to observers though

 

That's what I meant, just didn't word it well, electronics revision was making me depressed and giving up on good language.

[lakmilis]

Because it's a total scale change. It affects everything because everything is in essence made out of light - as demonstrated by pair production, wherein a gamma photon is transformed into an electron and a positron.

 

don't mix pair production from photon annihilation up with 'everything is in essence light'. Everything is indeed energy, but light and mass both appear on the other side of the equation right

 

electron and positron come from an annihilation ok, can you get 'everything',i.e. all other particles from there?

 

x

[swansont]

Because it's a total scale change.

 

You'll have to define what you mean by that, because at this point it's no more meaningful than saying, "it's magic."