I'm a rookie and I have a question about spacetime

[The Grassy Knoll]

I'm very new to this site and most assuredly and not a physicist (or a scientist) , but I have a question I'm hoping y'all can help me with.

If I were traveling at or near the speed of light for a set distance- say Andromeda and back, time will slow down for me relative to the static observer. For that observer, it would have taken me much longer to reach Andromeda and back- so either (to them) I wasn't traveling at or near the speed of light or (to them) Andromeda is much farther than postulated by the observer.

In other words, it takes me longer to get there and back (as observed) then it did for me to get there and back (as I observed it), so is there a formula that describes the relationship of speed to time? It seems it cannot be one-to-one as time cannot stop completely at the speed of light (or photons would arrive instantaneously from any point in the universe (in the photons frame of reference).

I apologize if this is terribly elementary and poorly stated, but it's really been bugging me.

 

[Nugatory]

If I were traveling at or near the speed of light for a set distance- say Andromeda and back,

You cannot travel at the speed of light, so as phrased your question doesn't work at all - it's equivalent to asking "How do I apply the laws of physics to a situation in which they don't apply?". However, we can easily fix this by considering only the "near the speed of light" case, so that's what we'll do.

If you google for "relativity time dilation" you will quickly find the formula that relates two clocks in motion relative to one another. However, that formula is remarkably unhelpful for understanding the roundtrip that you are describing; you'll need to study the "twin paradox" (more googling) and especially this FAQ.

Time cannot stop completely at the speed of light (or photons would arrive instantaneously from any point in the universe (in the photons frame of reference).

Photons don't have a frame of reference, so this problem never arises. This comes up often enough that it's also a FAQ: https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/. Informally, what's going on is that when you say "The frame of reference of <something>" you're really saying "A frame in which that <something> is not moving", and there can be no such thing because light moves at speed $c$ in all frames.

 

[jbriggs444]

The observed time (also known as "proper time") for a [constant speed] traveler can be determined from the coordinate time from an inertial frame in which the starting and ending points are co-located. The formula is $$t_{proper}=\frac{t_{coordinate}}{\gamma}$$ where the gamma ($\gamma$) is given by $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

It is common for popularizations to speak of time stopping at the speed of light. Technically it is undefined as @Nugatory explains here

Edit: speak of the devil...

 

[The Grassy Knoll]

Thank you both. The link for the Twin Paradox was especially useful. Thanks for the formula as well!

 

[Janus]

I'm very new to this site and most assuredly and not a physicist (or a scientist) , but I have a question I'm hoping y'all can help me with.

If I were traveling at or near the speed of light for a set distance- say Andromeda and back, time will slow down for me relative to the static observer. For that observer, it would have taken me much longer to reach Andromeda and back- so either (to them) I wasn't traveling at or near the speed of light or (to them) Andromeda is much farther than postulated by the observer.

In other words, it takes me longer to get there and back (as observed) then it did for me to get there and back (as I observed it), so is there a formula that describes the relationship of speed to time? It seems it cannot be one-to-one as time cannot stop completely at the speed of light (or photons would arrive instantaneously from any point in the universe (in the photons frame of reference).

I apologize if this is terribly elementary and poorly stated, but it's really been bugging me.

If you are traveling at near light speed relative to the Earth and Andromeda, then for someone on at either place, or at rest with respect to them your clock would run slow. So for them, it would take a bit over 2.537 million years for you get there and another 2.537 million+ years for you to get back. (Andromeda is 2.537 million light years away). During which time, you will age much less. If you were traveling at 0.9999999999c you would age a little less than 72 yrs on the round trip.
But for you, it is the Earth and Andromeda that is moving at 0.9999999999c relative to you, and there is another effect of Relativity to take into account, Length contraction. While you still measure your speed relative to Earth and Andromeda as being 0.9999999999c, you measure the distance between the two as only being a bit less than 36 light years, which is why, according to you, you only age 72 yrs during the round trip.

Now there is more to it than just that. Just having the formulas doesn't give you a feel for what's going on. Relativity isn't really about motion "slowing time", as it is about about how observers in relative motion with respect to each other measure time and space differently.

 

[The Grassy Knoll]

Thank you Janus. You sent me down the rabbit-hole of Length Contraction now, and I'm trying to understand it. But Length Contraction doesn't seem to apply to the spaces between objects, does it?

 

[PeroK]

Thank you Janus. You sent me down the rabbit-hole of Length Contraction now, and I'm trying to understand it. But Length Contraction doesn't seem to apply to the spaces between objects, does it?

Length contraction applies to any measured length. Whether you are measuring the length of an object or the distance between two objects.

 

[Janus]

Thank you Janus. You sent me down the rabbit-hole of Length Contraction now, and I'm trying to understand it. But Length Contraction doesn't seem to apply to the spaces between objects, does it?

That line of thinking comes from treating relativistic effects as something acting on objects when they move, rather comparing measurements between moving frames.

Consider the following thought experiment:
You have two objects separated by some distance. Right next to these objects but not connected to or touching them is a measuring stick that just reaches from one object to another. This whole arrangement is moving at some velocity that is a good fraction of the speed of light relative to an observer, in a direction parallel to the measuring stick. According to this observer, the objects and measuring stick must be length contracted. But if the length of the measuring stick decreases, but not the distance between the two objects, then the measuring stick will no longer span the entire distance between the objects according to our observer and its two ends won't reach the objects.

Now consider an ant riding on one of the objects. Relative to him, the measuring stick is not moving, so it should not be length contracted and the two ends always remain next to the objects. According to him, he should be able to step off the object, over to the measuring stick and then use it to walk to the other object.

But above we said that according to our first observer the measuring stick ends don't reach the objects. Thus if the ant steps off the object, he would be stepping off into empty space. We have two created two conflicting realities. One for the ant and the other for our observer. It is only if the observer also measures the distance between the objects decreasing along with the length of the measuring stick that we don't get this problem. In the end, it doesn't matter if the measuring stick is actually there or not, the observer must measure the distance between the objects as undergoing length contraction to prevent contradictions.