What is Contraction: Definition and 707 Discussions

Muscle contraction is the activation of tension-generating sites within muscle cells. In physiology, muscle contraction does not necessarily mean muscle shortening because muscle tension can be produced without changes in muscle length, such as when holding a heavy book or a dumbbell at the same position. The termination of muscle contraction is followed by muscle relaxation, which is a return of the muscle fibers to their low tension-generating state.Muscle contractions can be described based on two variables: length and tension. A muscle contraction is described as isometric if the muscle tension changes but the muscle length remains the same. In contrast, a muscle contraction is isotonic if muscle tension remains the same throughout the contraction. If the muscle length shortens, the contraction is concentric; if the muscle length lengthens, the contraction is eccentric. In natural movements that underlie locomotor activity, muscle contractions are multifaceted as they are able to produce changes in length and tension in a time-varying manner. Therefore, neither length nor tension is likely to remain the same in muscles that contract during locomotor activity.
In vertebrates, skeletal muscle contractions are neurogenic as they require synaptic input from motor neurons. A single motor neuron is able to innervate multiple muscle fibers, thereby causing the fibers to contract at the same time. Once innervated, the protein filaments within each skeletal muscle fiber slide past each other to produce a contraction, which is explained by the sliding filament theory. The contraction produced can be described as a twitch, summation, or tetanus, depending on the frequency of action potentials. In skeletal muscles, muscle tension is at its greatest when the muscle is stretched to an intermediate length as described by the length-tension relationship.
Unlike skeletal muscle, the contractions of smooth and cardiac muscles are myogenic (meaning that they are initiated by the smooth or heart muscle cells themselves instead of being stimulated by an outside event such as nerve stimulation), although they can be modulated by stimuli from the autonomic nervous system. The mechanisms of contraction in these muscle tissues are similar to those in skeletal muscle tissues.

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  1. D

    Unique Fixed Point: Proving F^3 is a Contraction

    Homework Statement Suppose F is mapping of a nonempty complete metric space into itself, and that F^3 = F o F o F is a contraction (o's denote composition). Show that f has a unique fixed point.The Attempt at a Solution Isn't this kind of a trick question? Suppose f does not have a unique...
  2. N

    Why does length contraction happen only in the direction of motion?

    Length contraction happens only in direction of motion. Never perpendicular to the motion. My questions are 1) Why is it so?. For an observer in the same frame, it would mean a meter scale to give 2 different results. If by some means he is able to calculate the difference won't he be able to...
  3. S

    Proving Contraction Mapping: T^n is a Contraction

    [b]1. prove that,if T is acontraction mapping then T^n is a contraction Homework Equations The Attempt at a Solution
  4. I

    How Does Relativistic Speed Affect Photon Wavelength Measurement?

    Homework Statement Spaceship Enterprise fires a photon torpedo at an approaching Klingon ship that has just decloaked. If the wavelength of this light beam as measured on the Enterprise is 616 nm what is the wavelength (in nm) as measured by the Klingon ship if the relative speed between the...
  5. A

    Non-linear length contraction

    hey forum, first of all, I'm a high school kid so forgive me if this is stupid. I've been thinking about relativity for some time now, and the issue with simultaneity. Einstein proposed that length contracts as you approach the speed of light. Assume for a second that a train is going...
  6. F

    Einstein's Length Contraction A problem?

    Hello, I hope you can help with my question! I am a 27 year old amateur theoretical physicist about to start a bachelor's degree in physics as a mature student... I have just been going over some bits of Einstein's theory of Special Relativity and have noticed something odd that has confused...
  7. S

    Time dilation and length contraction problem

    Homework Statement Anna is on a railroad flatcar moving at 0.6c relative to Bob. Her arm is outstretched in the dirction the flatcar moves, and in her hand is a flashbulb. According to her wristwatch, the bulb goes off at 100 ns. This even according to Bob differs by 27 ns. a) is it earlier...
  8. K

    Time dilation and length contraction in hyperbolically-curved spacetime

    For the universe to be totally flat, and not just asymptotically closer to being flat as the universe expands, wouldn't there have to be pockets of hyperbolically-curved spacetime? In either case, I still would like to know how one expresses time dilation and length contraction in hyperbolic...
  9. T

    Combining time dilation and length contraction

    So, I am having trouble understanding how time dilation and length contraction in special relativity merge together and describe space-time. I guess the best way to ask this question is to pose a question, which i know how to answer mathematically, but I would like to discuss some thoughts about...
  10. mrspeedybob

    Length contraction and the expansion of the universe.

    Start with the following 3 statements... 1. If I were traveling through the cosmos at high velocity relative to the CMB I should observe the distances between stars and galaxies to be length contracted in the direction of my motion, but not in directions perpendicular to my travel. 2. The...
  11. I

    Time Dilation/Length Contraction

    Homework Statement A Rocket Moves away from the Earth at a speed of (3/5)c. When a clock on the rocket says that one hour has elapsed, the rocket sends a signal back to the earth. (A). According to clocks on the earth, when was the signal sent? (B). According tot eh Clocks on the earth, how...
  12. A

    About confusion of lenght contraction, and possiblity of length expansion

    hello people... i have a doubt regarding Lorentz length contraction... according to what he described, the length of a body measured in a moving frame appears shorter as compared to the one taken by an observer at rest...if a train moving with uniform relativistic velocity , is thought of...
  13. J

    Contraction of the Riemann Tensor with the Weak Field Metric

    I have started with the space-time metric in a weak gravitational field (with the assumption of low velocity): ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2) Where \phi<<1 is the gravitational potential. Using the standard form for the Christoffel symbols have found: \Gamma^0_{00}=\phi_{,0}...
  14. J

    Contraction of the Riemann Tensor with the Weak Field Metric

    I have started with the space-time metric in a weak gravitational field (with the assumption of low velocity): ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2) Where \phi<<1 is the gravitational potential. Using the standard form for the Christoffel symbols have found...
  15. M

    Question on Michelson Morley experiment and length contraction

    I'm a lay person who is interested in developing a better understanding of science in general, as well as specific theories. I'm just wondering if someone would be able to help me understand how Length contraction explains the null set of the Michelson Morley experiment? Hopefully this...
  16. A

    Length Contraction: Observing Light Hits on a Train

    Regarding the observer riding on the middle of the train sees the light strike first the fwd first and then the aft. Will it be safe to say that for the observer to see the light strikes them both at the same time to adjust the tail of the train by shortening the train so that light can arrive...
  17. T

    Tensor transforming law problem / metric-delta contraction

    Hey guys it's me again! I'm now asking you 2 question, I'm sure you'll be helpful as usual! 1) changing basis- changing tensors ok, the law of transformation of a (let's make this simple) 02 tensor is g_{\mu '\nu '}=\frac{\partial x^\alpha}{\partial {x^{\mu}}'}\frac{\partial x^\beta}{\partial...
  18. W

    Complex scalar field and contraction

    Hi guys, If I use the definition of the scalar complex field as the combination of two scalar real fields, I can get \phi (x) = \int \frac{d^3 p}{(2\pi )^3} \frac{1}{\sqrt{2p_0}} [ \hat a _{\vec{p}} e^{-ip.x} + \hat b _{\vec{p}}^{\dagger } e^{ip.x}] which I can rewrite in terms of...
  19. M

    Volume Contraction (Water & Methanol Mixture)

    Hey there. I've been searching the internet on volume contraction with water and methaol mixture. Although I have found a little bit of infomation I don't know why it happens. I found it quite intriguing that mixing 50ml of water and 50ml of Methanol =/= 100ml of liquid. In fact there is a 4%...
  20. T

    Lorentz contraction in other dimensions?

    Hi guys, this is my first post/thread, so I'd like to start with an easy one:rolleyes: I've searched the web and I wasn't able to find a satisfying proof of the fact that Lorentz contraction is NOT applied to the dimensions, that are not parallel to the direction of motion (e.g...
  21. J

    Terrell Revisited: The Invisibility of the Lorentz Contraction

    Terrell Revisited: "The Invisibility of the Lorentz Contraction" I recently posted this response to a general question of how Special Relativity worked. G H Wells Jr pointed out that and Terrell's Argument Both of these are important issues to take into account. However, they do...
  22. A

    Length and Distance Contraction

    hi Just wondering if someone can clarify for me whether it is merely the length of a moving object that appears contracted to a stationary observer, or whether it is also the distance between the moving object and other objects in its direction of motion that appears contracted. Or is the...
  23. S

    Is length contraction an actual occurrence or merely an optical illusion?

    Hello everyone. I was thinking about length contraction in Special Relativity last night. I looked up information on the internet, and from what I understand, length contrtaction has never been measured (I'm not completely sure if I simply failed to find information to the contrary). So my...
  24. S

    Calculating Velocity Using Length Contraction Formula in Relativity Theory

    Homework Statement A spaceship moves past you at speed v. You measure the ship to be 300 m long, whereas an astronaut on the ship measures a length of 445 m. Find v. The Attempt at a Solution I tried to substitute my numbers into L1=Lsqrt(1/(v^2/c^2)) and keep getting a negative wrong answer...
  25. L

    What happens to the geometry of a spinning disk as it rotates about its center?

    If a circular disk rotates about its centre, what will happen to its geometry. Since a spinning disk has velocity gradients, different regions of the disk must contract by different proportions. For example, a uniformly moving body undergoes length contraction and its new geometry is easily...
  26. S

    When a protostar stops contraction

    It is written that when the gas of the protostar is completely ionized, it stops contraction and it gets into hydrostatic equilibrium. I don't understand why?
  27. U

    Length Contraction: Measuring Circumference of Moving Circle

    As I understand it, there is no length contraction in the direction perpendicular to the motion being described. So if I were to observe a circle moving along a line (not rostating) and I were to measure the radius in te direction parallel to the motion, I would observe a contracted radius, and...
  28. C

    Lorentz Contraction Physical Reality

    Simple thought experiment I read and would like to hear what others think will the result will be: Let two spaceships A and B accelerate along a straight line. Observer C does not accelerate. The accelerations, as judged by C, are constant for both ships. Each ship is equipped with a...
  29. R

    Length Contraction of the Universe Surpassing Length of Moving Object?

    A spaceship is of length 1000 meters (to the observer standing in the spaceship). It is traveling so close to the speed of light that to the observer in the spaceship, the 'length' of the universe has contracted to 900 meters. Q1: If I am the observer in the spaceship, what do I think the front...
  30. M

    Contraction of the canonical symplectic form by vertical vectors

    The canonical symplectic form on T^*M is the exterior derivative of the tautological 1-form: \omega=d\alpha where \alpha_p(X):=p(d\pi(X)) is the tautological 1-form. Let Y \in T_pT^*M a vertical vector, that is d\pi(Y)=0. It's trivial to prove using canonical coordinates that for...
  31. C

    Lenght contraction of a charged wire and time dilation?

    In my class we were doing examples with a current carrying wire and if we moved with a speed v we would see length contraction. And because of this the moving line charge would go up in value and we would see an Electric field. And then we did the same for a solenoid but he said we need to...
  32. D

    Quick question to clear up some confusion on Riemann tensor and contraction

    Let's say I want to calculate the Ricci tensor, R_{bd}, in terms of the contractions of the Riemann tensor, {R^a}_{bcd}. There are two definitions of the Riemann tensor I have, one where the a is lowered and one where it is not, as above. To change between the two all that I have ever seen...
  33. V

    Length Contraction and Time Dilation

    Length Contraction and Time Dilation Gamma= 1/sqrt(1-v^2/c^2) = 2 (Assumed) We have L=L’/Gamma…………………………………….1 And dT= dT’ * Gamma ………………………………2 Let primed frame is that of Bob and unprimed that of Dave. Let us define identity as an equation in which values on both...
  34. J

    Equations for length contraction

    So I was bored and decided to find some simple equations to deal with relativistic geometric edges and angles at an angle to the direction of movement. L=L_0\sqrt{(\frac{\cos(\Delta\theta_0)}{\gamma})^2+(1-\cos(\Delta\theta_0)^2)^2}...
  35. P

    Q: if you travel closer to c, will you see length(distance) contraction

    Q: if you travel closer to c, will you see length(distance) contraction between andromeda and earth?
  36. D

    Deriving Length Contraction From Lorentz Transform

    Homework Statement From Lorentz Transform, x^{\prime} = \gamma (x - vt) From textbooks and wikipedia, L_0 = x'_2 - x'_1 = \gamma (x_2 - x_1 ) Where x_1 and x_2 = L Thus, \L_0 = \gamma L Question is this: If i take the same method and us the Inverse Lorentz transform, i seem to...
  37. R

    Time dilation & length contraction

    Hi guys and girls. Need some assistance with these problems, not the hardest examples, but I need some help on the way. Homework Statement 1. An astronaut travels at 0.9c across our galaxy, which is 100 000 light years in diameter. How long time will it take (according to the...
  38. T

    General Tensor contraction: Trace of Energy-Momentum Tensor (Einstein metric)

    Okay so I have: Eqn1) Tij=\rhouiuj-phij = \rhouiuj-p(gij-uiuj) Where Tij is the energy-momentum tensor, being approximated as a fluid with \rho as the energy density and p as the pressure in the medium. My problem: Eqn2) Trace(T) = Tii = gijTij = \rho-3p My attempt: Tr(T) = Tii...
  39. F

    Contraction in the Riemann Tensor

    Hi all, I'm trying to follow through some of my notes of a GR course. The notes are working towards a specific expression and the following line appears: R^{\alpha \beta}_{\gamma \delta ; \mu} + R^{\alpha \beta}_{\delta \mu ; \gamma} + R^{\alpha \beta}_{\mu \gamma ; \delta}=0 Which by...
  40. M

    Length contraction Griffiths

    In Griffiths book (Intro to Electrodynamics, page 489) he uses one simple gedanken experiment with train, lamp and mirror, to prove the length contraction \Delta x'=\gamma \Delta x. My question is why he uses two directions of light and not just only one? For example, when we use, for observer...
  41. M

    Length Contraction causes Time Dilation?

    I had a big epic discussion on another board after someone stated that "if I were to travel to Betelgeuse at a sufficient velocity I would reduce the distance between myself and Betelgeuse until it is say, 2 light years, which means I would only experience 2 years or so during my journey", this...
  42. A

    How does the length contraction work for proper length?

    Well.. Proper length ,from my understanding, is the minimum distance between 2 events in any frame. Then, how does the length contraction work? suppose someone from other inertial frame try to measure the length.. The length will be contracted to L/gamma..shorter than proper length...
  43. G

    Specific relativity Length Contraction and Time dialation question

    Special relativity Length Contraction and Time dilation question Homework Statement Planet X is 18 Light Years from earth, A spaceship moving towards the Earth at a speed of 0.82C (Measured from Planet X) fires a series of 1.2 cm long and 2.1 gram mass (as measured by the pilot) projectiles...
  44. F

    Time dilation yes, why no contraction?

    The example I have read to show time dilation is that of a light clock on a train. Two mirrors are one metre apart. Light is beamed from the first mirror to the second. An observer on the train sees that it takes the amount of time for light to travel 1m for the light to reach the second mirror...
  45. N

    Time dilation and length contraction

    Can someone please clear this up for me? Lets say the distance of Point A from Earth is 10.4 light years. Some spacecraft is traveling 0.95c. So. The person in the spacecraft will see Earth contract but Earth will see the spacecraft contract in length too. The thing I'm confused on is...
  46. Y

    How to calculate the contraction of metric tensor g^ab g_ab

    I wish I could calculate the contraction: gabgab I wish someone could show me how to get n! Unfortunately, I find it difficult, for I am not familiar with Tensor Algebra ... My wrong way to calculate it: gabgab= gabgba (since gab is symmetric) = δaa = 1Why is it wrong?
  47. W

    Time Dilation: Does Length Contraction Apply?

    Suppose I am standing on the Earth surface and observing a rockhet of very high speed then i will see the length the rocket contracted and abserver on the rocket will also see my length contracted(I am not sure about it)in the direction of motion. Is the same case takes place with time...
  48. R

    Can Length Contraction be Proven Experimentally?

    Is length contraction an assumption which is verified experimentally or can it be proved? If it can be proved, how to prove it graphically? By proof, I do not mean demonstrate. I just want to prove length1=length2 * (gamma).
  49. P

    Length Contraction: Need Help Understanding Lorentz Transformation

    Hello! need some help with length contraction. So according to lorentz transformation we got I don't know how to put symbols so ill use Y as gamma since they look alike :) dx' = Y dx - u Y dt So proper length refers to the frame where dt = 0 since u are measuring the ends at the...
  50. H

    What would actually be observed during Lorentz contraction?

    Greetings everyone, I understand the derivation of the Lorentz transformations, and have not had trouble applying the concepts and the math to most elementary SR problems. However, something occurred to me recently which I have been unable to resolve. Let’s say there are two tennis balls...
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