Length (and Mass) vs. Time Dilation

[hemmi]

Hey, I've been trying to get my head around Special Relativity and I'm having some trouble with the Lorentz Transformations. I have the impression that the contraction of time, length, and mass are equal, but the contrary impression that the length contraction is an effect of *measurement* whereas time dilation is obviously (twin paradox) present. So if time really slows down, would an object actually compress? Or is the measurement, unlike time, the result of the light (perhaps distorted from motion of the object) reaching the observer? Thanks!

 

[pmb_phy]

Hey, I've been trying to get my head around Special Relativity and I'm having some trouble with the Lorentz Transformations. I have the impression that the contraction of time, length, and mass are equal, but the contrary impression that the length contraction is an effect of *measurement* whereas time dilation is obviously (twin paradox) present. So if time really slows down, would an object actually compress? Or is the measurement, unlike time, the result of the light (perhaps distorted from motion of the object) reaching the observer? Thanks!

Dear hemmi

I'd like to give you a big ole forum Welcome to the physics forums. Its a pleasure to have a new poster here. I hope this turns out to be a pleasant experience for you.

Now to work!

I have the impression that the contraction of time, length, and mass ...

I've never heard anyone say that mass contracts unless you're using the term "mass" to be "object" or "matter" as some people tend to do. In forums and newsgroups its best to define some terms so as to have a common language with everyone else. In this case it appears that you used the term mass to refer to a non-invariant mass. One that depends on the velocity of the mass relative to an observer. a lot of people call this "relativistic mass." I call it inertial mass as many textbooks in SR/GR do. Can you tell me what you meant by the phrase "contraction of mass"? Thanks.

As far as what "actually" happens, i.e. is it just a measurement or something real, gets to the roots of relativity. Define quantities in a way that specifies a way to measure them. In such a case the physical quantity is defined in terms of how its measured. That's called an operational definition. Lorentz contraction is about real phenomena and things actually become shortended into in the direction of motion. However nothing has changed as measured from the rest frame.

The Lorentz contraction can be derived only with the relationship for time dilation and length contraction. I've worked this out and placed it on my web site. See

Time Dilation
http://www.geocities.com/physics_world/sr/light_clock.htm

Lorentz Contraction
http://www.geocities.com/physics_world/sr/lorentz_contraction.htm

Lorentz Transformation
http://www.geocities.com/physics_world/sr/lorentz_trans.htm

I would hazard to guess that I haven't answered your question so with the above in mind please tell me how I cane help further? Thanks

Pete

 

[country boy]

In special relativity the trick is often to first understand simultaneity. Each observer will define the length of a stick by requiring that the positions of the two ends be measured at the same time (or something equivalent). But the moving observer and the stationary observer will not synchronize their clocks the same way. The difference in their definitions of simultaneity is what makes their two length measurements different. It may sound like just definitions, but they are not arbitrary.

 

[birulami]

So if time really slows down, would an object actually compress?

The canonical answer to this seems to be to ask back 'slow down with respect to what' and 'shrink with respect to what'? When starting to learn about SR, you likely react with puzzlement, because you think that the reference is obvious. The next step is to realize that the obvious reference you had in the sub-conscious back of your mind is not available --- this is relativity and all (inertial) reference frames are on equal footing.

After that you likely think to pick just any frame MY and proclaim that you want to know it 'with respect to MY'. Ok then, with respect to MY, the moving frame THY shows length contraction and time dilation. But wait. The other way around it is the same: with respect to THY, MY is moving and shows the same length contraction and time dilation. Which one is real, which one is a measurement effect. Are they both real? Are they both measurement effects?

The canonical answer is that you can't tell and that there is no point to further investigate.

A seldomly cited fact, already stated by http://en.wikipedia.org/wiki/John_Stewart_Bell"

admitting a special system of reference which is experimentally inaccessible, is consistent​

with Special Relativity.

Basically this means that if

1. you assume that there is one preferred frame ABS, and that
2. THY and MY move with different speeds in ABS, and
3. you therefore conclude they both have different real contraction and dilation (real = with respect to ABS)

it follows nevertheless that mutual comparison between THY and MY will turn out completely symmetric. The asymmetricly biased measurement rods and clocks will nicely turn out identical results like magic --- or like some math involving nothing more complicated than a square root and some care.

Even worse: it turns out that ABS joins the conspiracy of symmetry so that THY and MY will both conclude from their measurements of ABS that ABS suffers contraction and dilation.

Consequently the assumption of the absolute frame ABS leads to no new insight, except maybe the insight that it leads to no new insight, which I experienced as a very educational insight indeed. To gather more from the non-insight, see http://arxiv.org/abs/physics/0512196" .

Cheers,
Harald.

 

[hemmi]

Okay, let me first apologize for the belated response. I hope the future affords me more time to sit and ponder. Second, thank all of you for your quick, thoughtful, and welcoming replies.

Regarding "mass contraction" I meant quite the contrary. I was talking about the increase in apparent mass of a moving object. I think I got too caught up in the lorentz contraction.

Anyways, after reading your responses I am more comfortable thinking about objects and measurements with respect to other objects and measurements. However, before I move on, particularly with pmb_phy's links on the lorentz equations, I have a question on the derivation of time dilation with the light clock.

I feel that my "inner" perception of time should be independent of a beam of light. The only way I can convince myself that if I get into a spaceship and travel at near the speed of light that "my" time will slow down, is if, similar to the effect of the light clock - the light beam having to travel a greater distance "sideways" to have the effect of going back and forth between mirrors - I assume that every subatomic particle in my body has a correlation to the speed of light, and in order to keep up the consistency of the speed of light, slow down such that all the electric pulses firing in my brain, while normal to me, are actually acting much slower with respects to an observer not in the ship.

Sorry about the wording and please bear with me. This stuff is hard.

Thank you so much!

 

[pervect]

Your inner perception of time does not change if you get on a spaceship and travel at some high velocity near 'c'.

Time for you will always tick at the rate of 1 second per second.

It might be helpful to think about how one experimentally measures time dilation. Let us single out for the purposes of discussion one particular inertial frame, which we will call the lab frame.

The lab frame has an array of clocks, one every mile

(start)x----x----x----x----x----x----x----x----x(end)
twin T

These clocks are all synchronized. The process of synchronizing the clocks, however, depends on the frame, i.e. the clocks are synchronized in the lab frame, but will not necessarily appear synchronized in any other frame.

The traveling observer, T, starts out at the left of this array of clocks, and both the lab frame clock and the twin clock read 0 when the twin is at the leftmost clock.

The twin moves to the right at some high velocity 'v'. Every time the twin is at the same place as a clock in the lab frame, an observer in the lab frame writes down the time on the Twin's clock, and the time on his lab clock.

An observer on the Twin clock can do the same - he will write down exactly the same numbers as the lab observer.

All observers will agree that the time reading on the Twin clock is always lower than the time reading on the Lab clock adjacant to the twin whenever the twin is to the right of the starting point.

This illustrates time dilation - the lab observer concludes from this experiment that the Twin's clock is "ticking more slowly".

However, relativity says that the twin can set up the exact same experiment, switching the roles between the "twin" and the "lab frame" in the above outline.

The key to understanding relativity is to realize the the process of synchronizing clocks is not universal - that if the twin creates an array of clocks that share his velocity, and synchronizes them in his frame, that this array of clocks will NOT appear to be properly synchronized in the lab frame.

This has noting to do with the "perception of time" - time still ticks at the rate of 1 second per second for both the lab frame observer and the twin frame observer.

 

[jtbell]

The key to understanding relativity is to realize the the process of synchronizing clocks is not universal - that if the twin creates an array of clocks that share his velocity, and synchronizes them in his frame, that this array of clocks will NOT appear to be properly synchronized in the lab frame.

Similarly, in the traveling twin's reference frame, the Lab clocks are not synchronized. If the twin can somehow synchronize those clocks suitably in his frame, then both observers will agree that whenever a Twin clock passes a Lab clock, the Lab clock always has the lower reading. But now the Lab observer will object, "hey, those clocks aren't synchronized!"

 

[birulami]

I feel that my "inner" perception of time should be independent of a beam of light. The only way I can convince myself that if I get into a spaceship and travel at near the speed of light that "my" time will slow down, is if, similar to the effect of the light clock - the light beam having to travel a greater distance "sideways" to have the effect of going back and forth between mirrors - I assume that every subatomic particle in my body has a correlation to the speed of light, and in order to keep up the consistency of the speed of light, slow down such that all the electric pulses firing in my brain, while normal to me, are actually acting much slower with respects to an observer not in the ship.

Sorry about the wording and please bear with me. This stuff is hard.

Personally I like your wording very much. Lorentz' and FitzGerald's original explanation of length contraction is more or less based on this reasoning, namely that forces acting at the subatomic level act with speed c, and because they have to keep up with you traveling, only the "left over" part, which then must be less then c relative to the moving frame is available to mediate or act. Your conclusion that your time runs slower then (though you yourself would never feel this), is but half of the truth. The other half is length contraction. Interestingly, if you do the math, you find that length and width contraction but no time dilation would be a solution too. Only experiments tell us that the true solution is

1. length contraction,
2. time dilation,
3. no width change.

This Lorentzian reasoning, however, is frowned upon, because it implicitly or explicitly invokes an absolute reference frame with regard to which contraction and dilation are "real" in the sense described above (longer path of action on the subatomic level). At least you may learn from this picture easily, as you described yourself, that you should expect problems when naively comparing delta-times between different frames. That is why the synchronization of clocks is always explained in depth in the discussion of SR.

Harald.