geordief

Are there any philosophical -or other sorts of - implications from time dilation (esp the Twin Paradox)?

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This is a consequence of Special Relativity and ,although it has been empirically demonstrated it still seems "unreasonable" to common sense.

 

It seems like it is a fact of life nonetheless and I was just wondering can we generalize from the result or do we just take it "as is" and just apply it to such circumstances as it applies to directly.

 

I realize this question must have been asked on countless occasions. I don't think I have an agenda but hopefully I may learn something if anyone has a view;

Edited by geordief

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There are basically two competing philosophies about "twin paradox" time dilation, which happen to be discussed in detail in the parallel thread "Models for making sense of relativity - physical space vs physical spacetime"; in particular posts #1 (Langevin's interpretation as he introduced the "twin" astronaut scenario) and # 78 (comparing Lorentz ether explanation with Minkowski block universe explanation for the "twin" scenario).

 

In my opinion this thread is superfluous as it duplicates that one. But maybe you can think of something that would fit here, and that is not discussed (or going to be discussed) there.

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If something is empirically demonstrated then you have to throw away any preconceptions and adapt to the new result; evidence is king. As far as commonsense goes, it has no place in science; too unreliable.

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What time dilation tells us is that the old notion of time ticking away in the 'background' is not really the right way to view the Universe. A global time for everyone works okay for Newtonian physics - well this is actually written into the maths - but this is only an approximation and relativity gives us a deeper view of time.

 

Still, lots of things we don't really understand about time and its direction...

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This is a consequence of Special Relativity and ,although it has been empirically demonstrated it still seems "unreasonable" to common sense.

 

 

That is because common sense is (initially) forged by experience of the slow, low-energy world where your "reasonable" view is accurate enough. It shouldn't take very long for new information to modify our common sense understanding so I am always puzzled by why people struggle with this. The ideas have been around for over 100 years, now.

 

I remember reading about relativity when I was very young (possibly Gamow's Tompkins in Wonderland). I obviously didn't fully understand it, but maybe that early exposure is part of the reason that it just doesn't seem a particularly odd idea to me. It is just the way the world is.

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That is because common sense is (initially) forged by experience of the slow, low-energy world where your "reasonable" view is accurate enough. It shouldn't take very long for new information to modify our common sense understanding so I am always puzzled by why people struggle with this. The ideas have been around for over 100 years, now.

 

I remember reading about relativity when I was very young (possibly Gamow's Tompkins in Wonderland). I obviously didn't fully understand it, but maybe that early exposure is part of the reason that it just doesn't seem a particularly odd idea to me. It is just the way the world is.

I was always a very slow learner. Even now I am just learning that Maxwell's equations are not invariant under Galilean transformation........so not even up with the 19th century yet :(

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I was always a very slow learner. Even now I am just learning that Maxwell's equations are not invariant under Galilean transformation........so not even up with the 19th century yet :(

 

Concerning SR, it means that you are almost there! :)

If your math skills are not too poor, you can understand a derivation of the Lorentz transformations with your "19th century" knowledge.

 

However, that would be typically something to elaborate in the physics or relativity forums; thus I guess that a derivation is not what you are after.

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Concerning SR, it means that you are almost there! :)

If your math skills are not too poor, you can understand a derivation of the Lorentz transformations with your "19th century" knowledge.

 

However, that would be typically something to elaborate in the physics or relativity forums; thus I guess that a derivation is not what you are after.

I followed Einstein's simple derivation a few years back

 

http://www.bartleby.com/173/a1.html

 

It took me about 3 or 4 weeks :eek: but ,as you hint I think I would may find greater satisfaction in understanding and picking through the maths and the physics behind Maxwell's equations and the "invariance anomaly " as perhaps it is described.

 

Someone said that Maxwell would probably have worked out SR if he had not died too soon......

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Someone said that Maxwell would probably have worked out SR if he had not died too soon......

I think that could have been a possibility. For sure special relativity via the Poincare transformations is `written into' Maxwell's equations, as are other important things in modern physics like conformal invariance, gauge invariance and electromagnetic duality (in vacuum).

 

Maxwell's work really was the starting place of a lot of modern physics - so like Einstein and Lorentz's work on time dilation the philosophy of physics was changed by the understanding of the mathematics.

Edited by ajb

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You have asked about the popular phrase 'time dilation'.

 

This makes it very difficult to answer because strictly speaking time does not dilate.

 

It is the time interval or time difference or time lapse that changes.

 

This time difference is measured between two points, just as we measure length between two points.

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You have asked about the popular phrase 'time dilation'.

 

This makes it very difficult to answer because strictly speaking time does not dilate.

 

It is the time interval or time difference or time lapse that changes.

 

This time difference is measured between two points, just as we measure length between two points.

When you say that"strictly speaking time does not dilate" is that very close to or equivalent to saying that proper time is the same for every frame of reference ? (1 sec per sec is how I think it has been described)

 

And "Time dilation" is only a function of the relationship between two moving frames -how they each measure the time interval (as a component of the space-time interval ) in the other's frame of reference?'

 

Or are you saying something different?

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When you say that"strictly speaking time does not dilate" is that very close to or equivalent to saying that proper time is the same for every frame of reference ? (1 sec per sec is how I think it has been described)

 

And "Time dilation" is only a function of the relationship between two moving frames -how they each measure the time interval (as a component of the space-time interval ) in the other's frame of reference?'

 

Or are you saying something different?

 

When I say time does not dilate I mean :) time does not dilate.

 

The coordinates of a single event point are {x,y,z,t} in one observational coordinate frame and {x',y',z',t'} in another.

 

The values of x',y' z' and t' in terms of x, y z and t are given in a linear transformation.

 

Concentrating on time and considering that the t' frame is moving with velocity v parallel to the x (of the t frame) axis so we can drop the y and z

 

T' = At + Bx; where A and B are constants

 

So t' may be greater than, less than t or even negative depending on these constants.

 

Constant B allows for the fact that observers in t and t' may start counting time from different zero event points.

 

Introducing the relative velocity of the t and t' frames and doing some algebra leads us to

 

[math]A = \frac{1}{{\sqrt {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)} }} = \gamma [/math]
and
[math]B = - \frac{{\gamma v}}{{{c^2}}}[/math]
So we have exchanged constants A and B for two others, gamma and c.
Gamma is the Lorenz factor and is only valid for the combination of the two frames in question
c is the speed of light and is valid for all frames.
This is useful as these constants apply to the transformation of all four coordinates, not only time.
None of these linear transformations lead to a 'dilation' of the coordinates.
Noting that t and t' refer to the same event point we can answer the question what does dilate then?
I said you need two (event) points for this.
If we consider the difference between two points that is (x2 - x1) and (t2 - t1) in the first frame and (x'2 - x'1) and (t'2 - t'1) in the second frame
We have a length and a time difference.
Many physical quantities come in two flavours like this.
Electric potential and potential difference both measured in volts
Temperature and temperature difference both measured in degrees
Each of the two flavours have the same units but somewhat different characteristics and are used for different purposes in physics.
So back to relativity, these differences are taken between the same two event points (before we had one, now we have two points) but viewed in the different frames.
So we are talking about the same length and the the same time difference in both cases.
If you perform the Lorentz transformations on coordinates from one frame to yield the coordinates for both points in the other and take the length and time differences in each frame you will get different numbers.
So observers in each frame will evaluate these differences as being different numbers.
Alternatively if we substitute in the Lorenz transformations into my difference formula above (x2 - x1) and (t2 - t1) in the first frame and (x'2 - x'1) and (t'2 - t'1) in the second frame

we will obtain formulae for what happens when we consider the same time difference or distance difference (length) from the standpoint of difference frames.

 

In other words we will obtain the formulae called time dilation and length contraction.

 

One final note

 

These formulae are developed using linear or 'first order' analysis.

 

This is OK when the event points are close to each other and in particular the differences can become infinitesimals.

 

So [math]{\rm{\Delta t}}\;{\rm{and}}\;{\rm{\Delta x}}[/math] become [math]\delta {\rm{t}}\;{\rm{and}}\;\delta {\rm{x}}[/math]

This allows us to define, or assign meaning to, calculus operations involving relativity formulae.

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