Question regarding light from distant objects

[Robokop]

TL;DR Summary

How can we receive light from an object 10 billion light years away? Since the universe is expanding, wouldn't that source have been a lot closer to us 10 billion years ago. Meaning the light would have already reached us?

Given that the universe is expanding, and we currently believe the universe as we know it began a little over 13 billion years ago, Then when we look at a distant object and say we are looking light from 10 billion years ago, How is that possible. With the universe expanding for 13 billion years, then 10 billion years ago we all would have been closer together. And the light would have been coming from much closer and therefore would have already reached us.

 

[Vanadium 50]

How can we receive light from a flaslight 10 feet away? The same argument applies, no?

 

[Orodruin]

In cosmology you need to be very careful when you say ”an object 10 billion ly away” as this is not a statement that is constant over cosmological scales. The objects which emitted lights 10 billion years ago that we receive today were indeed closer than 10 billion light years at the time of emission. (The reason it took light 10 billion years to reach us is because the travel distance remaining expanded during the travel time.) However, they would be further away than 10 billion light years away today. (The distance already covered by the light also expanded after the light passing.)

 

[PeroK]

Summary:: How can we receive light from an object 10 billion light years away? Since the universe is expanding, wouldn't that source have been a lot closer to us 10 billion years ago. Meaning the light would have already reached us?

Given that the universe is expanding, and we currently believe the universe as we know it began a little over 13 billion years ago, Then when we look at a distant object and say we are looking light from 10 billion years ago, How is that possible. With the universe expanding for 13 billion years, then 10 billion years ago we all would have been closer together. And the light would have been coming from much closer and therefore would have already reached us.

How long light takes to travel from a source to a receiver depends on the initial distance and the expansion rate. If light is emitted from a star 1 billion light years away, then it will take more than 1 billion years to reach us, as the space between the source and receiver expands during the light's journey.

There will be some distance that corresponds to a time of 10 billion years. In a non-expanding universe it would be 10 billion light years. In an expanding universe it is less than 10 billion light years.

That said, you seem to assume that objects emitted a flash of light 13 billion years ago and have been dark ever since. Which is why @Vanadium 50 gave the answer he did.

 

[Robokop]

Thank you for the responses. I guess I was thinking of light more like a particle then a wave. I think I am getting a better understanding of it. If I think of the light coming from that object like a slinky, it gets stretched out as they move apart, but they are still connected (so to speak) but the slinky getting stretched out would be similar to the red shift.

 

[JimJCW]

Summary:: How can we receive light from an object 10 billion light years away? Since the universe is expanding, wouldn't that source have been a lot closer to us 10 billion years ago. Meaning the light would have already reached us?

Given that the universe is expanding, and we currently believe the universe as we know it began a little over 13 billion years ago, Then when we look at a distant object and say we are looking light from 10 billion years ago, How is that possible. With the universe expanding for 13 billion years, then 10 billion years ago we all would have been closer together. And the light would have been coming from much closer and therefore would have already reached us.

The questions you ask are complicated by the space expansion in the Big Bang model. Please allow me to divide them into two situations and I will answer the questions using Jorrie’s calculator based on PLANCK Data (2015):

1. Suppose we receive light from an object that is 10 Gly away. We want to know when the received light was emitted and the distance of the object from us at that time.
2. Suppose we receive light that has traveled 10 Gyr to reach us. We want to know when the light was emitted and the distance of the emitter from us at that time. We also want to know the distance of the emitter from us now.

Answer to Question #1:

The light was emitted 7.39 Gyr ago at a distance of 5.34 Gly from us at that time. It takes the light 7.39 Gyr to reach us. Now the emitter is at a distance of 10 Gly from us.​

Answer to Question #2:

The light was emitted 10 Gyr ago at a distance of 5.84 Gly from us at that time. It takes the light 10 Gyr to reach us. Now the emitter is at a distance of 15.84 Gly from us.​

 

[Robokop]

That is very interesting. Thank you for that. It is complex to think about.

 

[JimJCW]

1. Suppose we receive light from an object that is 10 Gly away. We want to know when the received light was emitted and the distance of the object from us at that time.

Answer to Question #1:

The light was emitted 7.39 Gyr ago at a distance of 5.34 Gly from us at that time. It takes the light 7.39 Gyr to reach us. Now the emitter is at a distance of 10 Gly from us.​

Using Jorrie’s calculator, we can obtain the following result about the journeys of the object and the light after they separated 7.39 Gyr ago at a distance of 5.34 Gly from us: the light propagating to us and the object moving with space expansion to its current location.

 

[Robokop]

Thank you. Your information is helpful. I really appreciate your response.