# I What is the physical cause behind time dilation?

#### David Lewis

You have a line segment in a 2D plane. As the line rotates, its width will decrease and its height will increase (or vice versa).

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#### sweet springs

Time dilation can be shown mathematically but what is the physical phenomenon due to which it occurs?
Let us see a bar on the ground. We go around the bar and find its length in our tranverse direction(x) and length in longtitudinal direction (y) varies according to what angle to the bar we are. Bar Length^2 = x^2 + y^2 is kept constant during our walk.

Time dilation is something similar to that. According to a kind of angle we take, that is moving speed to referring thing, time length (t) and space length(x) of a kind of bar, that is world line of referring thing, vary. World Line Length^2=t^2-x^2, or more fully, c^2t^2-x^2-y^2-z^2 is kept constant during our change of angle or taking various speeds to Thing. One plus and three minus signs in the formula touch the core of relativity.

#### David Lewis

The world line is that of the center of the bar, one end of the bar, a moving body, or something else?
Is the bar analogous to the spacetime interval, or something else?

#### Rap

There's no physical phenomenon, its a point-of-view phenomenon. It's like asking "when I look at circle head-on, it looks like a circle, but when I view it from an angle, it looks like an ellipse. What is the physical phenomenon which causes this?"

Different inertial frames have different "points of view", they divide spacetime up into space and time in different ways. People in different inertial systems disagree about the time between two events in the same way people viewing a circle at different angles will disagree on what it looks like. They both understand why they disagree, just as relativity explains why two inertial systems may disagree.

#### Mister T

Gold Member
Time dilation can be shown mathematically but what is the physical phenomenon due to which it occurs?
First of all, it cannot be shown mathematically. It's shown physically.

Secondly, what do you mean by the notion that it's due to some physical phenomenon? It is itself a physical phenomenon.

Ask yourself what physical phenomenon is responsible for the fact that the reading on a clock changes continuously?

#### PAllen

Ask yourself what physical phenomenon is responsible for the fact that the reading on a clock changes continuously?
Still in the analog world, are we?

#### Sorcerer

Ask yourself what physical phenomenon is responsible for the fact that the reading on a clock changes continuously?
If you want to know that, ask me, Sorcerer... because the answer is ~MAGIC!~

#### nitsuj

I know that things do not actually change size in their reference frames but only is observed to be doing so. I am asking if time dilation occurs due to the time taken by the light to reach us or something of that sort.
I like the perspective it's the geometry of spacetime; however that is one step after the most favored irreducible reply, that c is invariant. Am surprised no one mentioned causality. That's a fun one to think of as being the cause of time dilation / length contraction.

For a simply put book on SR, Relativity (a brief insight) by Russell Stannard is one I like. He put's a fair amount of emphasis on measurement (in turn perspectives); which I find important when developing an understanding of the concept in general.

#### Ebeb

There's no physical phenomenon, its a point-of-view phenomenon. It's like asking "when I look at circle head-on, it looks like a circle, but when I view it from an angle, it looks like an ellipse. What is the physical phenomenon which causes this?"

Different inertial frames have different "points of view", they divide spacetime up into space and time in different ways. People in different inertial systems disagree about the time between two events in the same way people viewing a circle at different angles will disagree on what it looks like. They both understand why they disagree, just as relativity explains why two inertial systems may disagree.
There's also the Block Universe interpretation:
The physical phenomenon is not that one looks at a physical 3D object from a different point of view, but rather that one observes a different cut through a physical 4D 'spacetime' object.

(To follow your circle/ellips comparison: the ellips is not a different view of the circle, but a cut at a different angle though a cylinder)

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#### robphy

Homework Helper
Gold Member
I like the perspective it's the geometry of spacetime; however that is one step after the most favored irreducible reply, that c is invariant. Am surprised no one mentioned causality. That's a fun one to think of as being the cause of time dilation / length contraction.

For a simply put book on SR, Relativity (a brief insight) by Russell Stannard is one I like. He put's a fair amount of emphasis on measurement (in turn perspectives); which I find important when developing an understanding of the concept in general.
I would have mentioned causality and other things but I was too busy to comment and the thread has gone on for a while now.
But since you mentioned causality...
I would say that the big idea in relativity and spacetime, at the deepest level, isn't the Lorentz group but it is the causal structure.
And there are some interesting papers along these lines.

"Causality Implies the Lorentz Group"
Journal of Mathematical Physics 5, 490 (1964); https://doi.org/10.1063/1.1704140
E. C. Zeeman

"A contribution to chronogeometry"
Canad. J. Math. 19(1967), 1119-1128 https://cms.math.ca/10.4153/CJM-1967-102-6
A. D. Alexandrov

"Zeeman topologies on space-times of general relativity theory"
Communications in Mathematical Physics, October 1976, Volume 46, Issue 3, pp 289–307 https://doi.org/10.1007/BF01609125
Rüdiger Göbel

and likely what first inspired this line of thinking was

"The Absolute Relations of TIme and Space" (1921) and "The Geometry of Time and Space" (1936)
https://archive.org/search.php?query=creator:"Robb,Alfred+A."
A.A. Robb ( https://en.wikipedia.org/wiki/Alfred_Robb )
where he used the notion of "after" (a partial order relation) to try to "derive" Minkowski spacetime.
Robb introduced the notion of "rapidity" is relativity.
His "Optical Geometry of Motion" (1911) https://archive.org/details/opticalgeometryo00robbrich is surprisingly insightful for 1911, just a few years after Minkowski (1907) and Einstein (1905). You can see aspects of the radar method in it.

#### David Lewis

It sounds like you are invoking a mechanical metaphor by using the word rotation, but I can't follow what you are saying (and I am not implying that is your fault). Can you clarify?
"Hermann Minkowski developed the concept of three-dimensional space combined with time to form a four-dimensional space-time. The importance of this concept is that... the effect of relative movement... appears in the same manner as does the effect of a rotation in three-dimensional space." -- Dr. Ron Davis

#### sweet springs

appears in the same manner as does the effect of a rotation in three-dimensional space."
Coordinate transformation for rotation is given by, say $\theta$ is rotaion angle,
$$x'=x\ cos\theta + y\sin\theta$$
$$y'=-x\ sin\theta + y\cos\theta$$
which satisfies the relation
$$x'^2+y'^2=x^2+y^2$$

Similarly that of boost is given by, say $\theta=\frac{v}{\sqrt{1-v^2}}$ where dimensionless v is $v=V/c$
$$ct'=ct\ cosh\theta + z\sinh\theta$$
$$z'=-ct\ sinh\theta + z\cosh\theta$$
which satisfies the relation
$$c^2t'^2-z'^2=c^2t^2-z^2$$

cosh and sinh are hyperbolic cos and hyperbolic sin.

#### sweet springs

EDIT
For boost
$$tanh\theta=v=V/c$$,
$$\theta=tanh^{-1}v$$

#### FactChecker

Gold Member
2018 Award
It is just an explanation of how the space-time coordinate system that we perceive and measure things in works. I don't know if you want to call that a physical thing or a mathematical thing.

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#### sweet springs

EDIT^2 to post#37
$$z'=ct\ sinh\theta+z\ cosh\theta$$

#### David Lewis

"It is sometimes said that length contraction occurs because objects rotate into the time axis. This is actually a half truth, there is no actual rotation of a three dimensional rod, instead the observed three dimensional slice of a four dimensional rod is changed which makes it appear as if the rod has rotated into the time axis. In special relativity it is not the rod that rotates into time, it is the observer's slice of the worldtube of the rod that rotates."

#### pervect

Staff Emeritus
A bit of a necropost (revival of a old thread, where the OP has most likely moved onto other topics) here , the latest post being on july 25 2019, the previous post on Nov 4 2018.

"What is the physical cause behind time dilation?"

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