Time Dilation & Length Contraction: Physics Explained

[xAceKing]

TL;DR

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So basically i know almost nothing about physics but i have this one curiosity and i hope you can help me ahah. For what i understand if you could move at the speed of light time would stop for you and you would see the whole universe age in a blink of an eye. But what if you could stand completely still? I know its impossible but if you stood completely still in the universe how much faster would time pass for you compared to everyone? How much slower would you see everyone move in %?

 

[etotheipi]

if you could move at the speed of light time would stop for you

You can't move at the speed of light w.r.t. some inertial observer, because you've got mass. It doesn't even make sense to speak about anything like the "rest frame of a photon", which doesn't exist, if that was what you had in mind. As it stands, then, this question is based on a false premise.

But if you moved at some non-zero speed $v$ less than $c$, w.r.t. some inertial observer, then you would actually see the wristwatch of the other observer ticking more slowly, not more quickly. Your wristwatch, on the other hand, would appear to tick at exactly one second per second.

But what if you could stand completely still?

Relative to what?

 

[vanhees71]

One should keep in mind that one shouldn't talk about "rest mass" in relativity but rather name it "invariant mass" and call that quantity (and only that quantity!) mass. Then the photon has simply $m_{\gamma}=0$.

 

[jbriggs444]

So basically i know almost nothing about physics but i have this one curiosity and i hope you can help me ahah. For what i understand if you could move at the speed of light time would stop for you and you would see the whole universe age in a blink of an eye. But what if you could stand completely still? I know its impossible but if you stood completely still in the universe how much faster would time pass for you compared to everyone? How much slower would you see everyone move in %?

Unfortunately, this simplistic picture of special relativity, though popular, is completely incorrect.

The first problem with the picture is minor: No massive object can move at the speed of light. But we can get around that. You can move at 99.9999% of the speed of light.

The second problem is more serious. No matter how fast you move, you can consider that you are at rest and that it is everything else that is moving. From your point of view, the laws of physics work just the same for you as they always did. Time would not slow down for you. You could look at your wristwatch and see it ticking at its normal rate.

This is the principle of relativity -- that the laws of physics are the same, no matter how fast someone else thinks you are moving. This principle has some powerful consequences. One consequence is that it is impossible to tell how fast you are moving. The only speeds that are physically meaningful are relative speeds -- how fast you are moving relative to something else.

The third problem is difficult to explain briefly and clearly. It is how time dilation actually works. To begin with, we need the idea of a "frame of reference". Suppose that you are floating out in the middle of space with a freight-car full of rulers and clocks. You have no way to determine your speed, so you pretend that you are at rest. You set one of the clocks down and declare that it is at the center of your coordinate system -- the "origin". You pick three orthogonal directions to be your "east", "north" and "up" and lay the clocks out in a rectangular grid aligned with those directions.

You synchronize all of the clocks using light signals so that the measured speed of light (distance between two clocks divided by the difference between the start time as recorded on the sending clock and the finish time as recorded on the receiving clock) is the same, no matter which pair of clocks is used.

You now have a four dimensional coordinate system covering a region of space-time. If you want to know the coordinates for where and when a particular event occurred, you find the clock that is nearest to that event. The x, y and z coordinates of the event are the x, y and z coordinates of the clock. The t coordinate of the event is the reading on that clock when the event occurred.

Time dilation is the fact that if you hurl a clock through your clock array and compare its time reading to a succession of readings of the clocks it is passing, the effect is as if the moving clock is running slow compared to the array.

It is important to realize that this "time dilation" is symmetric. If someone else has their own array of clocks and one of your clocks passes through their array, the comparison of your clock to their array will show your clock running slow.

The resolution to this seeming paradox is clock synchronization. You will not agree that the clocks in the other fellow's array are synchronized properly. The other fellow will not agree that yours are.