# Lorentz Contraction

I don't understand why this happens. And it's not enough to tell me 'well it happens because Simultaneity is relative' or 'Because Time dilates between frames'. I can still say I don't understand why it happens because shouldn't 2 frames adjust their measurements so that they get the same proper length?

Can someone explain, as this is the only SR concept that I don't understand very well.

HallsofIvy
Homework Helper
Actually, neither time nor simultaneity have anything to do with it. The real answer is "that is what experiment shows". In fact, Lorentz himself derived that formula by asking himself, "Given that the Michaelson-Morley experiment gives a null result, what must be true?"

Al68
I don't understand why this happens. And it's not enough to tell me 'well it happens because Simultaneity is relative' or 'Because Time dilates between frames'. I can still say I don't understand why it happens because shouldn't 2 frames adjust their measurements so that they get the same proper length?
Yes, every frame can calculate an object's proper length and get the same answer. Lorentz contraction means that the coordinate length, not proper length, of an object depends on the coordinate system (frame) used.

For example, if the proper length of an object is 10 meters, then in a reference frame in which the relative velocity is 0.8c, its coordinate length will be 6 meters, while its proper length will be 10 meters as calculated by either frame. Coordinate length equals proper length only for an object at rest in the applicable frame.

Why does the frame moving at velocity 0.8c measure 6 meters in the first place?

Why when you look at objects from distance, they appear to be smaller?

When you move, you look at spacetime from a different angle. So you measure the proper length differently.

Why when you look at objects from distance, they appear to be smaller?

When you move, you look at spacetime from a different angle. So you measure the proper length differently.

At last, a reasonable explanation as to why this happens. Was fed up with the waffly crap my textbooks kept giving me. This is just like parallax right?

Thanks ;)

A.T.
At last, a reasonable explanation as to why this happens.
Actually physics never tells you 'why' just 'how much'. What Dmitry67 wrote is just a geometrical interpretation of 'how much'. The object is rotated in space-time and we see only the shortened projection onto space. Here an animation:

JesseM
At last, a reasonable explanation as to why this happens. Was fed up with the waffly crap my textbooks kept giving me. This is just like parallax right?

Thanks ;)
It's not a visual thing like parallax--when Dmitry67 said "you look at spacetime from a different angle" he presumably wasn't talking about what you see visually, but rather the way the plane of simultaneity in your rest frame is oriented at a different angle from the one in the frame where you're moving. This page has a good primer on spacetime diagrams in SR, and here's a diagram from that page illustrating why different frames measure length differently:

Actually, neither time nor simultaneity have anything to do with it. The real answer is "that is what experiment shows". In fact, Lorentz himself derived that formula by asking himself, "Given that the Michaelson-Morley experiment gives a null result, what must be true?"

Hopefully, you understand MMX does not prove the light postulate.
This is a common misconception.

MMX is consistent with light emission theory.

One such attempt is known as the Emission Hypothesis (or the ballistic theory of light), and was developed partly by Walther Ritz (C&N p.353). According to this theory, light behaves like bullets shot from a gun, its speed with respect to the source being a universal constant and independent of any ether. This idea is consistent with the null results of the Michelson-Morley experiment and many others.
http://laser.phys.ualberta.ca/~egerton/specrel3.htm [Broken]

Problems with emission theory
The simplest form of emission theory says that radiating objects throw off light with a speed of "c" relative to their own state of motion
http://en.wikipedia.org/wiki/Emission_theory

Modern Physics/Michelson-Morley Experiment
Walter Ritz's emitter theory (or ballistic theory), was also consistent with the results of the experiment
http://en.wikibooks.org/wiki/Modern_Physics:Michelson-Morley_Experiment [Broken]

This paper shows emission theory is consistent with SR.
http://arxiv.org/PS_cache/physics/pdf/0512/0512036v1.pdf

This rules out any conceptually coherent ballistic theory of light propagation, according to which the speed of light is the vector sum of the velocity of the source plus a vector of magnitude c. Ironically, the original Michelson-Morley experiment was consistent with the ballistic theory, but inconsistent with the naïve ether theory, whereas the Sagnac effect is consistent with the naïve ether theory but inconsistent with the ballistic theory. Of course, both results are consistent with fully relativistic theories of Lorentz and Einstein, since according to both theories light is propagated at a speed independent of the state of motion of the source.
http://www.mathpages.com/rr/s2-07/2-07.htm

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JesseM
Hopefully, you understand MMX does not prove the light postulate.
This is a common misconception.

MMX is consistent with light emission theory.
Other experimental evidence is inconsistent with the emission theory, though.

Other experimental evidence is inconsistent with the emission theory, though.

Also, Sagnac is inconsistent with emission theory.

This rules out any conceptually coherent ballistic theory of light propagation, according to which the speed of light is the vector sum of the velocity of the source plus a vector of magnitude c. Ironically, the original Michelson-Morley experiment was consistent with the ballistic theory, but inconsistent with the naïve ether theory, whereas the Sagnac effect is consistent with the naïve ether theory but inconsistent with the ballistic theory. Of course, both results are consistent with fully relativistic theories of Lorentz and Einstein, since according to both theories light is propagated at a speed independent of the state of motion of the source.
http://www.mathpages.com/rr/s2-07/2-07.htm

JesseM
This paper shows emission theory is consistent with SR.
http://arxiv.org/PS_cache/physics/pdf/0512/0512036v1.pdf
I didn't try to analyze this paper too carefully but I get a crackpotty feel from it, note on p. 4 where he writes "Einstein’s concept of a clock that one tick of the clock always represents one second in moving inertial frames is wrong and leads to the clock paradox or twin paradox as pointed out in Ref.[9]." (Ref. 9 being another paper by the same author) The standards for getting a paper on arxiv.org aren't so high, there's a lot of stuff on there that would never pass peer review. In any case, on pp. 4-5 the author says that the notion of light's velocity depending on the source only makes sense if you are using the "quasi-velocity" rather than the normal coordinate velocity in a given frame, the quasi-velocity apparently being defined by change in position in the moving frame divided by time in the stationary frame.
Now, we see the light velocity c (m/s), instead of light quasi-velocity (m/tick), is independent of the relative velocity due to the relativity of simultaneity. Since Ritz’s emission theory [8] involves the light quasi-velocity (m/tick) dependent of the source, the theory is consistent with the postulate of constancy of light velocity except the Lorentz factor 1/gamma.

I didn't try to analyze this paper too carefully but I get a crackpotty feel from it, note on p. 4 where he writes "Einstein’s concept of a clock that one tick of the clock always represents one second in moving inertial frames is wrong and leads to the clock paradox or twin paradox as pointed out in Ref.[9]." (Ref. 9 being another paper by the same author) The standards for getting a paper on arxiv.org aren't so high, there's a lot of stuff on there that would never pass peer review. In any case, on pp. 4-5 the author says that the notion of light's velocity depending on the source only makes sense if you are using the "quasi-velocity" rather than the normal coordinate velocity in a given frame, the quasi-velocity apparently being defined by change in position in the moving frame divided by time in the stationary frame.

Yes, I admit I do not like it either.

But, I supply it for a full comparison.

I believe we need to look at every angle and some are very suspect like this one.

For example, if Ritz's theory is consistent with SR, then why does light from moving light sources show no increase in the speed of light.

But, again, I need to supply what I have found.

A.T.