It is generally believed that time dilation and length contraction is a geometric effect, is there anyone has tried to explain the time dilation and length contraction effect in a geometric way?
Albert Einstein is said to explain the time inflation effect in this way:
"When you sit with a nice girl for two hours you think it’s only a minute, but when you sit on a hot stove for a minute you think it’s two hours. That’s relativity."
Time dilation and length contraction are consequences of space and time being combined into one entity called spacetime and this is a true physical fact. Thus if you travel at the speed of light like a photon,you reach any place at the same time you leave your place since photons do not experience time and for them space is contracted to zero.
More details are given by Astrophysicist Neil deGrasse Tyson in this short Nat-Geo William-Shatner YouTube video: https://youtu.be/u8lx19V7SNg?si=DdwNf8bB52ieuO2j
I found one elegant illustration to time dilation and distance contraction, which I personally use each time I speak about it.
Consider Eucludean space E^3 and a plane in it. Then consider a linear segment of length b whose one vertex lie on plane and another is outside it. Let the angle between the segment and plane is phi. Now, we can project the segment to plane using orthogonal projection. The projection image (the "shadow") of the segment has the length b * cos(phi) < b because cos(phi) < 1. Similarly, we can project the segment to the line orthogonal to plane and compute the projected length.
In the space-time (Minkowski space M^(3,1)) the computing is the same except angles between space and time component is hyperbolic. So, if some time-like interval t is considered in different reference system, that is, projected to different time-like axis, its length ("shadow") in new reference system is t * cosh(phi) > t because cosh(phi) > 1. This is the effect of time dilation. The hyperbolic angle phi is the angle between the world lines of segment t and new reference system time. Its physical sense is v / c = tanh(phi), where v is the relative speed between these two reference systems and c is the speed of light.
Now, if we want to compute the dilation coefficient in terms of v and c, we need to represent cosh(phi) using tanh(phi):
1 - tanh^2(phi) = 1 / cosh^2(phi),
cosh(phi) = 1 / sqrt(1 - tanh^2(phi)) = 1 / sqrt(1 - v^2 / c^2).
That's pretty all.
“Can the mechanism of time dilation and length contraction of the special relativity be explained?”
- the really scientific explanation of the relativistic properties and effects “time dilation” and “length contraction” is quite short: in the realty any “time dilation” and “length contraction” fundamentally cannot, and so don’t, exist.
Matter’s spacetime completely for sure is absolute – that completely directly, rigorously and unambiguously follows from that from the SS postulates
- that there is no Matter’s absolute spacetime; and that all/every inertial reference frames are absolutely completely equally equivalent and legitimate,
- any number of really senseless consequences completely directly, rigorously and unambiguously follow, though to prove that some theory is wrong it is enough to point only one senseless consequence. In this case utmost simple and evident is the Dingle objection to the SR.
Really , as that rigorously scientifically shown in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, Matter’s utmost universal “kinematical” spacetime is fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [5]4D spacetime with metrics (at least) (cτ,X,Y,Z,ct).
So, say, Matter’s spacetime fundamentally isn’t really imaginary [mathematically] 4D Minkowski space, which is “contracted” , “dilated”, etc.
Correspondingly any attempts “to explain” the effects in the SR can result only in something as
“…These 'effects' are a consequence of the math. They are explained by the math. To understand them you have to understand the math...”
- mathematics isn’t physics, and to understand “them” it is necessary to understand physics. That is another thing, that in the mainstream physics the SR is standard theory, despite that the effects are completely ad hoc postulated by Minkowski his own illusions – in this case he postulated that letters x,y,s,t, in Lorentz transformations relate to all/every points in Matter’s spacetime,
- and by this simple, mathematically completely perfect, but physically fundamental fantastic, way “discovered” the effects;
- having for this fundamentally only some completely transcendent imagination about what the words “space”, “time”, “Matter”, “Lorentz transformations” , really mean. That is another thing that mainstream physics till now has the Minkowski imagination above, and so some Astrophysicists, say, tells populace about unbelievably weird things that happen in Matter, say
“…Time dilation and length contraction are consequences of space and time being combined into one entity called spacetime and this is a true physical fact. …photons do not experience time and for them space is contracted to zero.….”
- though all really only some mystics in the quote by any means fundamentally cannot, and so don’t, really exist.
More about what are the really scientific physical meanings of these words see linked above paper.
To read SS posts in
https://www.researchgate.net/post/How_do_we_understand_special_relativity/2 , pages 1,2
https://www.researchgate.net/post/Am_I_wrong_when_I_correct_Einsteins_Relativity_by_addressing_Einsteins_error_in_the_Twin_Paradox/5pages 3,5,6
https://www.researchgate.net/post/Why_is_space_3-dimensional#view=663be33b56679de777075893/1/2
https://www.researchgate.net/post/Do_events_invoke_time_in_space pages 1,2
- it is useful as well.
Cheers
It seems as worthwhile to add some comment to the SS post above [though that below is in the links in the posts] that relates to point – yeah, the Minkowski postulate that the letters x,y,z,t in Lorentz transformations mean all/every points in Matter’s spacetime is, of course, wrong, but to what do these letters really relate?
The answer is – the Lorentz transformations relate only to coordinates of points of rigid bodies, which the bodies occupy in the 3DXYZspace at current time moment, t.
As that is, of course, also in Galileo transformations, where the letters above relate to points that passenger, table, chairs, cutlets, flies, etc. in a Galileo cabin on a ship occupy - as, equally that is/happens in a tavern on a beach;
- and these points by no means relate to other spacetime points in Matter’s absolute spacetime, where the cabin and tavern are.
At that an observer in the tavern can describemotions of what is/happens in the cabin, i.e. compose equations of motion of, passenger, table, etc., by two ways:
– he can directly, by using his instruments, measure in his reference frame coordinates x,y,z, t, velocities, time intervals, of what is in the cabin at rest and moves inside it,
- and to measure directly only the velocity and coordinates of the cabin, further using the coordinates x’,y’,z’, t’ , velocities, time intervals, of, say, cutlets, flies, which are measured by the passenger, and Galileo transformations between x,y,z, t, and x’,y’,z’, t’; t’=t
Both ways are completely equally equivalent, besides that the 2-nd way is in many cases more convenient.
Lorentz transformations by no means differ from the Galileo ones, besides the fact, that if a cabin, after been heavily impacted by some external force and accelerated moves with large speed, the passenger’s rules, distances between chair, cutlets, flies, etc.,[and chair, cutlets, flies, etc.], are really contracted, and clocks in the cabin tick slower, comparing with rulers, clocks, etc, in the tavern,
- so to link in the 2-nd way above adequately to the reality x,y,z, t, and x’,y’,z’, t’; t’ not equal to t; it is necessary to apply Lorentz transformations.
At that, again, in both frames both, x,y,z, t, and x’,y’,z’, t’, relate only to same physically points of the same passenger, table, chairs, cutlets, flies, etc. in the cabin, and fundamentally by no means relate to any other Matter’s fundamentally absolute spacetime points; which [spacetime] fundamentally cannot be “contracted”, “dilated”, “curved”, etc.
More see the SS post above and links in the post, here only note also, that that above is rigorously completely adequate to the reality only if the tavern is an absolute inertial reference frame, i.e. it is at rest in the absolute 3D space,
- while everything in Matter fundamentally exists and happens only in the absolute spacetime, and completely independently on – what something what measures in what frame; and on some such somethings exist or not at all, though.
Correspondingly measured values of parameters of what really exists and happens in Matter are real only if are measured in absolute frames, while measured in any moving in the space frame the values are unreal. However till now, because of action of really extremely Galileo-Poincaré relativity principle , absolute motion isn’t observed,
- but if instruments in a reference frame, i.e. rulers, and synchronized in accordance with the principle distant clocks, compose a rigid system, the measured unreal values are completely adequately to the reality applicable in everyday physical practice.
Cheers
In addition to the above responses, i want to mention that it is generally agreed on that length contraction is a real effect (see e.g. Bell's spaceship "paradox" https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox), and the twins "paradox" can be easily solved by drawing the worldlines of the twins and play with different accelerations.
A very good book for both beginners / non-physicists as well as confused experts (that very well know the math but have trouble with the interpretation / meaning) is "Philosophy of Physics: Space and Time" by Tim Maudlin (https://press.princeton.edu/books/paperback/9780691165714/philosophy-of-physics).
Also, a look into the historical debate / correspondence between Newton, Leibniz and Clarke as well as Mach is worthwhile.
All the best.
“…In addition to the above responses, i want to mention that it is generally agreed on that length contraction is a real effect (see e.g. Bell's spaceship "paradox" https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox)....”
- that the FitzGerald-Lorentz contraction of moving bodies is real follows from the 1887 M&M experiment, the null result of which was explained by FitzGerald as that the M&M interferometer arm length, when the arm is directed along Earth motion with speed V ~ 30 km/s direction , becomes to be contracted in (1-V2/c2)1/2 . Though if FitzGerald would know that Earth moves in space with speed ~370 km/s, as that now follows from CMB dipole [and the arm is directed along the dipole axis], he would obtain the same explanation for this speed.
The Bell paradox relates not to the FitzGerald-Lorentz contraction of [rigid] bodies, but to “space contraction” that is postulated in the Minkowski theory, which is standard SR theory in mainstream physics, while, say, at least Lorentz never believed that this relativistic effect exists, and this paradox reveals that the “space contraction” really don’t exist, even in framework of the SR;
- and the Bell paradox is real consequence from that the SR “space contraction” postulate is fundamentally wrong.
As well that
“…and the twins "paradox" can be easily solved by drawing the worldlines of the twins and play with different accelerations….”
- is wrong. The twin paradox is really two times applied Dingle objection to the SR, from which it rigorously follows that the SR postulates that there is no absolute Matter’s spacetime and that all/every inertial reference frames are absolutely equally equivalent and legitimate are fundamentally wrong, Matter’s spacetime really is absolute [see SS post above];
- while acceleration changes in this case nothing. More about what is twin paradox see https://www.researchgate.net/publication/322798185_The_informational_model_twin_paradox
Correspondingly that
“…..A very good book for both beginners / non-physicists as well as confused experts (that very well know the math but have trouble with the interpretation / meaning) is "Philosophy of Physics: Space and Time" by Tim Maudlin (https://press.princeton.edu/books/paperback/9780691165714/philosophy-of-physics). …”
- really is rather strange recommendation. The linked in the quote book is some one of thousands of equally really unphysical publications that tell about really non-existent whole complete validity of standard SR/GR.
For those readers, who really want to understand what is fast bodies mechanics, Lorentz transformations, etc., see the couple of SS posts above and links in the posts
Cheers
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