# Special Relativity and Distance/Space

• kgreen
In summary, the conversation discussed the concept of Special Relativity and how time and distance are relative depending on the frame of reference. The speed of objects can appear to slow down when in motion, and the length of objects can also appear to change. The concept was further clarified using examples of moving meter sticks and a spacecraft traveling at nearly the speed of light.
kgreen
I'm currently reading Brian Greene's The Fabric of the Cosmos. I have a question about Special Relativity. I understand that time slows down when there's relative motion. I wanted to ask something about distance/space. When time slows down, does that mean that, e.g. the speed of a car, slows down too? I'm new to studying physics. I'm sure this question can be easily answered. Thanks in advance!

Actually that's a tricky question. And not really well defined, although don't blame yourself ;-) If you explicitly describe a specific physical situation, we can tell you what you would see in it, but there isn't really anything to say about e.g. the speed of a car in general.

To say that "a car slows down" or to talk about the speed of a car at all, without saying in what frame it is measured is meaningless. That's the first lesson of "relativity".

In reference to a person who's stationary. I want to understand how distance is relative.

I am really starting to dislike this phrase "time slows down." I started out perfectly fine with it, but it certainly seems to engender a large amount of confusion. The phraseology makes it seem as though speed is absolute. I'm starting to get irritated by Brian Greene as well.

It would be better to phrase it like "clocks run slow when they are measured to be in motion." When a clock is moving, relative to you the observer, then you will observe that it runs slower than your own clock. Your question is asking if time dilation makes really fast things start going really slow as they get faster. Hopefully, saying it like that makes the answer obviously no.

In reference to a person who's stationary. I want to understand how distance is relative.

There is no such thing as "stationary" in an absolute sense. Whether a body is stationary or not depends on your frame of reference.

That does answer my question. Thank you! Could someone give me a simple example of how distance is relative when moving relative to one another?

kgreen said:
That does answer my question. Thank you! Could someone give me a simple example of how distance is relative when moving relative to one another?

You observe that moving meter sticks (again, moving relative to you) are shorter than your own meter sticks, in the direction of their motion.

For instance, take the twin paradigm in which a spacecraft travels from the Earth to Vega at nearly c. The Earth observer observes the clocks on board to run too slowly, and the ship to be shorter than the pilot does. So when he reaches Vega, his clock has only ticked a few seconds (let's say) even though in the Earth's reference frame, the trip took ten years.

On the other hand, the ship pilot considers himself to be at rest and the Earth and Vega to be in motion. His observations are that the Earth's clocks are running slower than his own. Nevertheless, he explains the fact that he arrives at Vega in only a few seconds by the fact that the distance between Earth and Vega is very small, much smaller than the Earth observer's measurement of 10 light years.

Thanks!

## 1. What is the concept of time dilation in special relativity?

Time dilation is the phenomenon where time passes differently for objects moving at different speeds. According to special relativity, time is relative and can be perceived differently by different observers depending on their relative speeds. This means that an object moving at a higher speed will experience time passing slower than an object at rest.

## 2. How does special relativity explain the concept of length contraction?

Length contraction is the phenomenon where the length of an object appears shorter when it is moving at high speeds. This is because, according to special relativity, the distance between two points in space is also relative and can be perceived differently by different observers depending on their relative speeds. This is why an object in motion appears shorter in length than the same object at rest.

## 3. Can special relativity explain the concept of space-time?

Yes, special relativity is the theory that explains the concept of space-time. It states that space and time are not separate entities, but are interconnected and can be perceived differently by different observers depending on their relative speeds. This theory revolutionized our understanding of the universe and paved the way for further research in the field of physics.

## 4. How does special relativity impact our understanding of the speed of light?

Special relativity states that the speed of light is constant and is the same for all observers, regardless of their relative speeds. This means that the speed of light is the ultimate speed limit in the universe and nothing can travel faster than it. This theory has been extensively tested and has been found to be consistent with all experimental results.

## 5. Can special relativity be applied to objects moving at very high speeds, such as spacecraft?

Yes, special relativity can be applied to objects moving at very high speeds, such as spacecraft. In fact, it is essential to take into account the effects of special relativity when dealing with objects moving at speeds close to the speed of light. This theory has been applied in various space missions and has been found to be accurate in predicting the behavior of objects moving at high speeds.

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