Is a length contraction just a visual thing?

Here's a nice paper that is relative.
http://www.physics.usyd.edu.au/teach_res/hsp/u5/t5_length.pdf

RELATIVE LENGTH: LENGTH CONTRACTION
Contraction takes place in the direction of motion only

Muon decay Experimental evidence for time dilation and length contraction

 

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Shouldn't it be

l=σX?
or

l=σK?

if a body is moving away x is a variant


''You are a stationary observer in an inertial frame of reference. A train was initially at rest in your frame of reference and you measure its length. However, when the train is in motion your measurement of its length is shorter. There is a contraction in its length. The train is shorter when it is in motion, but just as high and wide as it was at rest (figure 1).''


That is just not true and varifiable by the experiment I suggested.

 

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If we go slowly, you will never catch up.

K is free parameter in test theories of space-time that span Galilean Relativity, Newtonian Absolute Space and Time and Special Relativity.
In Galileo's/Newton's description of physics, K=0. In Special Relativity, \(K = \frac{1}{c^2}\). Galileo's and Newton's experiments were too slow and imprecise to distinguish the difference between these quantities.
In the test theory, we simply write K and let experiment decide what value of K best matches the data.

(Test theory) Space-time transformation in one-dimension of space: \( \Delta x' = \frac{ \Delta x - u \Delta t }{\sqrt{ 1 - K u^2 }} \\ \Delta t' = \frac{ \Delta t - K u \Delta x }{\sqrt{ 1 - K u^2 }}\)

The evidence for a particular value of K comes from precision experiments designed to test aspects of this relation:
(Test theory) Law of composition of velocities in one dimension of space: \(v_3 = \frac{v_1 + v_2}{1 + K v_1 v_2}\)

In 1859, it was empirically discovered that when \(v_1 \approx 10^8 \, \textrm{m} \cdot \textrm{s}^{-1}\) that \(K= \frac{1}{c^2}\) was preferred. This formula is derived from the Space-time transformation, so evidence for the latter is evidence for the former.​

(Test theory) Law of Proper elapsed time (time dilation): \(\Delta \tau = \sqrt{1 - K v^2} \Delta t\)

Experiments on unstable particles and clock in fast-moving vehicles such as satellites and jets have strongly supported \(K= \frac{1}{c^2}\). This formula is derived from the Space-time transformation, so evidence for the latter is evidence for the former.​

(Test theory) Law of co-moving distances (length contraction): \(L' = \sqrt{1 - K v^2} L_0\)

Observations on unstable particles created at the top of Earth's atmosphere reaching the ground and the engineering of synchroton radiation devices have strongly supported that fast-moving particles treat lengths as contracted and so \(K= \frac{1}{c^2}\) wins. This formula is derived from the Space-time transformation, as in my earlier post, so evidence for the latter is evidence for the former.​

(Test theory) relation between kinetic energy and momentum: \(\frac{p^2}{E - E_0} - 2m = \sqrt{m^2 + Kp^2} -m \approx K \left( \frac{p^2}{2m} - \frac{K p^4}{8 m^3} + \frac{K^2 p^6}{16 m^6} - \dots \right)\)

In the 60's they raced electrons to measure their momentum and energy. \(K= \frac{1}{c^2}\) wins. This formula is derived from the Space-time transformation, as in my earlier post, so evidence for the latter is evidence for the former.​

So we, unlike Newton's assumptions, appear to live in a world where \(K\) is non-zero and is approximately \( 1.11265 \times 10^{-17} \, \textrm{m}^{-2} \cdot \textrm{s}^2 = 11.1265 \, \textrm{TJ}^{-1} \cdot \textrm{mg}\) in SI units. But those numeric value are not natural inventions but represent our human choice to describe the world in certain units.

Because \(K\) is ubiquitous, it is common for college textbooks to choose a particular unit of time or distance as a standard unit and then choose the other so that when K is expressed in those units is the dimensionless value 1.

Example: In atomic physics, we might choose 1 Bohr radius as the standard unit of length and then \(\sqrt{K} \times 1 \, \textrm{Bohr radius}\) would be the standard unit of time. In such units, a speed below 1 is slower than light.

Another constant, say the reduced Planck constant, \(\hbar\) allows expression of mass in terms of the standard unit of length and physical constants. Likewise, adding a third, say Newton's constant of Universal Gravitation, G, means all combinations of length, time and mass can be expressed in combinations of physical constants which presumably results in human size numbers while studying realms of physical behavior where the units are decidedly not human-scale.

The concept is common in university-level instruction in physics for physics majors.

 

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Nup, wrong again......
https://www.loc.gov/rr/scitech/mysteries/universe.html

When scientists talk about the expanding universe, they mean that it has been growing ever since its beginning with the Big Bang.
The galaxies outside of our own are moving away from us, and the ones that are farthest away are moving the fastest. This means that no matter what galaxy you happen to be in, all the other galaxies are moving away from you.

However, the galaxies are not moving through space, they are moving in space, because space is also moving. In other words, the universe has no center; everything is moving away from everything else. If you imagine a grid of space with a galaxy every million light years or so, after enough time passes this grid will stretch out so that the galaxies are spread to every two million light years, and so on, possibly into infinity.

The universe encompasses everything in existence, from the smallest atom to the largest galaxy; since forming some 13.7 billion years ago in the Big Bang, it has been expanding and may be infinite in its scope. The part of the universe of which we have knowledge is called the observable universe, the region around Earth from which light has had time to reach us.

One famous analogy to explain the expanding universe is imagining the universe like a loaf of raisin bread dough. As the bread rises and expands, the raisins move farther away from each other, but they are still stuck in the dough. In the case of the universe, there may be raisins out there that we can’t see any more because they have moved away so fast that their light has never reached Earth. Fortunately, gravity is in control of things at the local level and keeps our raisins together.

Who Figured This Out?

The American astronomer Edwin Hubble made the observations in 1925 and was the first to prove that the universe is expanding. He proved that there is a direct relationship between the speeds of distant galaxies and their distances from Earth. This is now known as Hubble’s Law. The Hubble Space Telescope was named after him, and the single number that describes the rate of the cosmic expansion, relating the apparent recession velocities of external galaxies to their distance, is called the Hubble Constant.

So, is the Universe Infinite?

It might be easier to explain about the beginning of the universe and the Big Bang Theory, than to talk about how it will end. It is possible that the universe will last forever, or it may be crushed out of existence in a reverse of the Big Bang scenario, but that would be so far in the future that it might as well be infinite. Until recently, cosmologists (the scientists who study the universe) assumed that the rate of the universe’s expansion was slowing because of the effects of gravity. However, current research indicates that the universe may expand to eternity. But research continues and new studies of supernovae in remote galaxies and a force called dark energy may modify the possible fates of the universe.
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The Universe is expanding my friend: That's what the overwhelming evidence and everyone on this forum, along with your's truly has been trying to get you to see.
The scenarios you have fabricated are just that: fabrications.
You ignore the data and evidence in favour of your personal fabrications.
You are uncredentialed and an amateur lay person just as I am. The difference being I have chosen to read up on cosmology for many years, and see the logic and sensibility of what the many giants of the present and past, have worked out for us to build on.....when I say "us", I mean of course the working scientists and physicists, not the would be's if they could be's, that chose to spread their crankdomism on forums such as this.

You have no evidence what so ever that invalidates expansion.
You have no evidence at all that even comes close to invalidating time dilation, length contraction, validity of all FoR's and SR/GR.
Last time I looked, everything was as per normal and standard cosmology had proceeded leaps and bounds along with recent discoveries. And you remained a nobody...sorry.

 

No actually totally true and as verified many thousands of times by professional experts.

 

Agreed. The extended life is in Earth's frame. The space contraction is in the muon's frame. The muon "sees" a very contracted atmosphere, with earth's surface rushing up at it at almost the speed of light. If it could be scared, it certainly would be and the earth's mass is much greater in its frame. The first cyclotron confirmed the mass increase with speed as soon the particle was travleing in a circular path as nearly constant speed, yet the magnetic field causing it to curve had to continue increasing in strenth as it gained energy and mass.

about 13.5 billion years ago the diameter of the just formed universe was less than the current distance to the sun from Earth. We can only see back in time to a some what later date, when it was larger. Because before that all mater was in a plasma state, (or did not yet exist -too high a temperature) and a plasma is a very effective scatter of radiation, so just looks like a hot quite uniform surface (seen from an interior point) as it surrounds us. (Nothing special about us – it surrounds every point in the universe.)

The expansion of the universe, is now known to be accelerating but why it is, is not well known - that is the foundation of the dark energy postulate (does not really explaining anything - just giving a convenient name for something we don't yet understand. So named as normally acceleration is done by something expending energy.)

The universe is much bigger now than it was billions of years ago and we appear to have reached a stage in stellar evolution process (running out of large H2 clouds) that the number of stars is certainly not increasing. The distance between any typical pair is increasing (observation) so the average stellar density is decreasing (averaged on a very large scale).

If the average separation between raisins in a loaf of bread is increasing as it bakes, you can (and should) conclude the volume of the bread is increasing - i. e. it is expanding. Apply this same logic to the increasing average space between stars and conclude the universe is expanding.

 

I understand what absolute time dilation is and how it is effected within the gravitational energy field and across the radial gradients in that field due to altitude. I also am aware of the relative time dilation which is an artifact of observers in relative motion.

And, since reading a wiki reference posted by James R to danshawen in another thread, I am aware of the relative motion effects on images constructed from light information from objects moving relativistic speeds relative to an observer (eg, Terrell Rotation etc, which is an artifact of the image received, not a real representation of actual physical state or length parameters of the relatively moving object itself).

But I am still unclear what the claims are regarding the Muon often posted as an example of real physical contraction. I ask any learned member across these matters to please be so kind as to answer the following question for me:

Is it claimed that the in line cross section of the Muon itself shortened along the line of forward motion; or is it claimed that the forward, in line distance the Muon has travelled since its creation in the upper atmosphere to our underground detectors, that has shortened? Thanks.

 

http://www.atmosp.physics.utoronto.ca/people/strong/phy140/lecture32_01.pdf
SUMMARY Muons - An Example of Time Dilation and Length Contraction
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http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html
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https://en.wikipedia.org/wiki/Time_dilation_of_moving_particles
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http://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
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Both are _claimed_ but only the latter is claimed to have been demonstrated.

In the frame of reference dictated by our common standard of rest, the muon is perceived to be fast-moving and long-lived by a factor gamma, while any length-contraction is a contraction of a length too small to be distinguished from zero at rest.

In the frame where the same muon is at rest, we are fast-moving, the atmosphere is length-contracted in the direction of our motion by a factor gamma, and the muon lives only a normal short life.

 

http://physicsforidiots.com/physics/relativity/

 

You might want to look into a little theory referred to as "General Relativity". It not only presents an alternative to your idea, it also has an amazing amount of evidence.

 

Well, no you are back to being a buffoon who is merely denying the science, rather than a buffoon who is accepting the science but adding your own mystic interpretation on top.

You are not merely ignorant. Like most cranks, you hold your own ignorance with pride.

 

rpenner:

Thanks, rpenner, for your kind response. Very informative post, and from an obviously learned member.

Thanks. I understand now that it is a claim and only one aspect has been tractable to possible experimental confirmation.

I understand that also now. Thanks. Is it the pure relative speed through spacetime itself, or is it the absolute velocity in the frame of reference of the gravitational energy field, which determines the Muon lifetime when moving relativistically towards Earth?

I now pose the same question as above, except switching the Muon and Earth. Such a switchabout leads me to consider the actual object doing the moving through the atmosphere and the gravitational field.

What I mean is, I can apply logical motional and energetics analysis to the Muon moving through the atmosphere and gravitational field energy expanse, but how can I apply such a motional and energetics analysis to Earth which is effectively relatively 'static' when comparing their motions through the spacetime underlying the atmosphere distance and gravitational energy field extent?

The Earth is not moving through the same spacetime as the Muon, because Earth is obviously not moving through its own atmosphere and gravitational energy field which extend over the spacetime distance which the Muon actually traverses in fact and not merely in relative SR terms.

Can you see my dilemma? If I just accept the SR perspective, I cannot make a physical observation based on which is actually moving and which is actually relatively stationary in the Muon and Earth dynamics.

Can you help me progress past that dilemma, rpenner? I would be very grateful. Thanks.

 

He is not the only one I'm afraid...sad.

 

The analysis does not materially depend on the distortion in spacetime. This can be heuristically demonstrated by comparing the gamma factor minus 1 derived from relative speed in Special Relativity with the ratio of the product of the Schwarzschild radius of the Earth times the height of the atmosphere with the square of the radius of the Earth. Alternately one is free to do the full calculation in General Relativity to at least 12 digits precision if one expects to distinguish effects due to curved space-time.

The phrases marked in red reflect a conceptual model which has nothing to do with Special or General Relativity. In Special Relativity, there can be no such thing as a speed relative to spacetime. Likewise, in General Relativity there cannot be such a thing as absolute velocity for the reason that the symmetric solutions of the Schwarzschild solution are misleadingly vivid. Actual General Relativity admits far more coordinate maps than the Schwarzschild solution and describes space times that are obviously too cluttered to have a preferred standard of rest.

Your question is outside the bounds of this thread which is on Special Relativity and outside the framework of muons being short-lived particles which have a standard lifetime in their own rest frame. Indeed, there is no study of motion or energy as the muons have uniformly been assumed to be moving completely inertially, so the stopping power of the atmosphere is irrelevant.

Red herrings of negligible import.

That is not the issue. The muon, too, has a gravitational field. Neither the muon or the Earth has any claim in Special or General Relativity to be the standard of rest, but either qualifies to be a standard of rest. Globally, to the extent that SR describes the behavior, and locally, if you use the fully General theory.
But as the GR effects are wholly negligible, the atmosphere is thin to the point of being effectively transparent, and your conceptualization of a gravitational energy field is aphysical, it looks like you are seeking to sabotage your own study of physics.

To the extent that you have miseducated yourself on the nature of special and general relativity and perhaps physics itself, you need to shut up and calculate everything. Autodidacts frequently skip over the comparable coursework so when their understanding is compared to the well-educated they suffer in applying the knowledge they picked up from books.
If you can't calculate it, you probably don't understand it and need to discard your partial understanding in favor of remedial education. This self-education process mirrors the progress of physics as the history of relativity and quantum physics have shown us sometimes the only way to make progress is to back up and move in a new direction.

 

rpenner:

Thanks for your kind response, rpenner. I am not well and am returning to bed now. Tomorrow if I'm feeling better I will definitely peruse very carefully your post and come back with maybe further questions consequent to your very helpful and learned reply above. Thanks.

 

Where do you presume I am ignorant? It is you who are ignorant and have not got a clue about science. the ''buffoon'' as you put it trying to get an insult in to hide your stupidity, who accepts that some theories have been done, knows the difference between a theory and a fact, which clearly you have no idea the difference in.
I don't believe in God for the fact I have never observed a God, therefore factually a God does not exist, likewise I do not believe space is expanding, why do you think that is?

We have never observed space expanding, Fact

So stop continuing in your lies saying it is fact that space is expanding, we do not preach in science.

 

It looks complex, not because I do not have the ability to learn it , because I have no idea what it means or for what purpose it used, could you please explain the purpose of it?

I like formulas and standard maths such has F=ma , simple and of true value.

My own sort of maths starts here d=4/3 pi N³ a n-dimensional universe. Light radius and visual universe I do L=4/3 pi r(c)³ where c represents light.

Both formulas being an invariant to begin with.

The 1st formula an empty volume no matter what its volume amount is.


The second formula becoming a variate relative to a bodies motion.

Another forum did some maths which I can't post here, that shows the distance it would take for the sun to travel away from the earth before it '' vanished''beyond contraction point and light diminish.

Relative to either observer, it is them that is moving, relative to either observer, the other observer is contracting.



Observe the relativistic affect of the contraction and red shift of light, observe the stationary reference frame of the ''background'' does not contract. The object relatively moving away , is stretching the light by linear distance or angle of the incident ray, causing the light to narrow to single x axis so narrow, we can't observe the object any more.

I know GR and SR and Lorentz, I just don't know your maths to it. The very same reason space is not opaque, the bandwidth of electromagnetic radiation propagating through space is simply to narrow to see. e.g 0

 

Hi ****,

Confused2's muon experiment.

In the Earth frame there are two counters, one above the other separated by x metres (somewhere between 5,000 and 10,000 metres - doesn't matter. We know the speed of the muons so we know how long it takes then to travel between the counters - call that time t.

On the Muon ship the crew are sitting about and/or sleeping when suddenly they find themselves all standing up. The reason will become clear later (if not already). The science officer logs the time of this first standing up event. They settle down for a bit and then again - all standing up. Call the interval T between the first standing up event and the second standing up.

I give in. They stood up to be counted.

In the Earth frame the distance between the first count event and the second count event is x and the time interval is t where t= x/v
In the Muon ship the distance between events is zero and the time between events is T.

From reading millions of relativity books we know s²=x²-c²t² and s²=-c²T² where s is the invariant spacetime interval between the two events.
so we can write down
T= ???
Or not.

 

I can't understand what your are asking sorry,to be honest your analogy is not great.

Firstly you are saying we have two sensors(counters) a length apart, a Y-axis ?


Between these counters are falling muons or bi-directional Muons?

The rest I can't follow sorry, can you put it another way please?