# Explaining Special Relativity's Time Dilation

• TheIsland24
In summary, the spaceship taking off from Earth would appear to have passed by while only days have gone by on Earth. Time on the spaceship appears to be moving more slowly than time on Earth, and this is because the speed of light is always constant for an observer no matter the speed they are travelling.
TheIsland24
I've really been trying to understand the concept of time being relative in special relativity. I keep hearing the example of a spaceship taking off from Earth and traveling 99.999% the speed of light. It is said that possibly 200 years could pass for an observer on Earth while only days could pass for those on the spaceship. This makes absolutely no sense to me. If 200 years have passed on Earth and the spaceship hasn't returned, then it has been gone for 200 years. Can somebody please try and explain this to me.

There are two sorts of time in special relativity - coordinate time and proper time.

Coordinate time and coordinate space are labels that one can assign to any event. There are many different ways of assigning them to events in a way that make the laws of physics look "standard". Because all these different ways make the laws of physics look equally "standard", each way is as good as any other, and therefore we say coordinate space and time are relative.

Proper time on the other hand is absolute - but personal. The person on Earth has his personal clock, and the person in the spaceship has his personal clock. It is the "personalness", and not really any sort of "relativity", of proper time that makes less time pass for the spaceship than the earth.

I'm not a physics major, but here's the way I always pictured it in my head that makes sense to me:

First, the passage of time is always relative to the observer. Don't make the mistake of thinking that time is a universal constant. It's not. It's like a river. Water flows by at different speeds throughout the river, but never travels back the opposite direction. (i.e. water flows faster toward the center of the river than it does near the banks)

Second, the speed of light is always constant to the observer regardless of the speed at which that observer is travelling. For that mater, (aside from conceptual differences), the passage of time is always constant to the observer as well.

So, since the speed of light is constant from any reference frame, and the passage of time for the observer within that reference frame is always constant, then the only way for the speed of light to remain constant within any reference frame is for the passage of time with that reference frame to change accordingly. This is where time dilation comes in and is the cause of the 200 year difference.

A person never notices the difference in his or her own dilation in the passage of time. That person can only observe differences in a reference frame different than his/her own.

So, to the example of the spaceship traveling at 99.999% the speed of light, even though he is traveling that fast, time has dilated so much for him that if he measures the speed at which light travels, it will still seem to travel at the same 286,000 (approx.) miles per second that we measure it at here on Earth because we measure that speed in units of time.

On another note:
This is the same reason why it is believed that mass cannot meet or exceed the speed of light. No matter how much you accelerate mass, time continues to dilate for that mass, so acceleration continues to be less and less effective (from the point of view of an observer). It's like taking the number 1, and constantly cutting it in half. No matter how many times you cut it in half, you never reach zero. You just continue to get smaller and smaller fractions of 1.

TheIsland24 said:
I've really been trying to understand the concept of time being relative in special relativity. I keep hearing the example of a spaceship taking off from Earth and traveling 99.999% the speed of light. It is said that possibly 200 years could pass for an observer on Earth while only days could pass for those on the spaceship. This makes absolutely no sense to me. If 200 years have passed on Earth and the spaceship hasn't returned, then it has been gone for 200 years. Can somebody please try and explain this to me.

I think that one of the approaches can be like this:

In classical mechanics,we treat time is one of the natural laws. After 20th century, we know that time is a concept of human beings.

So the sets of coordinates that we use to describe physical laws/ natural laws need to be change a little bit:

before: natural laws are time,energy,lagragian,hamiltonian..,etc and coordinates are
t + (x,y,z) <-this is well-known

after: natural laws are energy,lagragian,hamiltonian..,etc (no 'time' anymore) and coordinates are
(ct,x,y,z)

The "after" uses time to describe natural laws. So one uses the coordinate (ct,x,y,z)
to describe natural laws.

We ,human, use light to observe the world, so speed should not be greater than light.
Just like when you save money to a bank , your saving must not be more than the total value of the bank ! (if can )

speed can be briefly known as x/t. So we with (ct,x,y,z)[1 watch + 3 rulers] and speed of light as a limit,we can only describe the world by for example increasing x +increasing t or decreasing x ,decreasing t or increasing some x +increasing some y +decreasing some z increasing some t to keep the total change be constant.

And finally the rocket problem! because u know from experience that it is very very.. fast,close to speed of light,so we need to increase so many t and increase so many x from your 1 watch + 3 rulers.and that is so call time slows down. remember time and space are your material not the outside world. So no matter how our time our space changes,the outside world- sun still rises as usual ,rainbow still has 7 colours, growth of animals...- the natural laws are still there.

@@hope these thing can help you to approach this

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## 1. What is time dilation in special relativity?

Time dilation is a phenomenon predicted by Einstein's theory of special relativity, which states that time runs slower for objects in motion relative to an observer. This means that time passes at a different rate depending on the relative speed of the observer and the moving object.

## 2. How does time dilation work?

Time dilation occurs because time and space are not absolute, but are instead relative to the observer's frame of reference. As an object moves faster, it experiences a "slowing down" of time due to the curvature of space-time. This effect becomes more noticeable as the object approaches the speed of light.

## 3. What is the equation for time dilation in special relativity?

The equation for time dilation is t' = t / √(1 - v^2/c^2), where t' is the time experienced by the moving object, t is the time experienced by the observer, v is the relative velocity between the two, and c is the speed of light.

## 4. How does time dilation affect our daily lives?

While the effects of time dilation are not noticeable in our daily lives, they are crucial for the functioning of technologies such as GPS. The satellites in the GPS system are constantly moving at high speeds, and without accounting for time dilation, the GPS signals would be inaccurate by several kilometers.

## 5. Is time dilation the same as time travel?

No, time dilation and time travel are two distinct concepts. Time dilation is a real phenomenon that occurs due to the nature of space and time, while time travel is currently only a theoretical concept that has not been proven to be possible. However, time dilation does play a role in many theories of time travel.

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