B New Paradox Discovered, I Think

[Somoth Ergai]

No. This is not correct.

What is correct is that you will see the light from the entire journey of the ship, from launch to arrival, arrive at your location in a much, much shorter time interval than 2 million years. The light signals all still arrive in order--you see the launch, then the journey, then the arrival, all in their proper order. The ship arrives just after the last light signal emitted during its journey.

How much shorter is the time interval in which you see all this? The relativistic Doppler formula tells us that For $v = 0.99999999999$ (in units where $c = 1$), the formula gives for the Doppler factor $f$:

$$
f = \sqrt{\frac{1 + v}{1 - v}} = \sqrt{\frac{1 + 0.99999999999}{1 - 0.99999999999}} = 447214
$$

The time interval $\tau$ during which you see the light signals all arrive is then the journey time $T$ divided by $f$, i.e., for $T$ 2 million years, we have

$$
\tau = \frac{T}{f} = \frac{2000000}{447214} = 4.47
$$

So you will see the light from the launch at Andromeda 4.47 years before the spaceship arrives, and during that 4.47 years you will see all of the light signals emitted by the ship during its journey, in order.

OK, I think I think I'm starting to understand. The issue i'm having is wrapping my head around how it could be that we could see an object which is in actual fact traveling slower than c appear to be traveling faster than c. I understand that you're telling me this is the case. I'm needing help understanding why though. conceptually I mean.

 

[Dale]

Actually it was post #3 by @Ibix.

Oops, yes it was.

The OP’s response was (IMO) unacceptable

we would have to see light traveling faster than itself. This does not resolve the situation

”I don’t understand” or “wouldn’t this mean” or “can you show me how” would have all been more productive

 

[Ibix]

Actually, it's about 4.47 years. Remember you have to take the square root in the relativistic Doppler formula. See my post #45.

I think we're calculating different things. In the Earth frame the flight time of light is 2 million years; the flight time of the ship is approximately one part in $10^{11}$ longer. Thus the arrival time of the ship is one part in $10^{11}$ of 2 million years after the light - about ten minutes. The Doppler analysis invokes ticks of the shipboard clock, which I'm not doing.

 

[Orodruin]

I think we're calculating different things. In the Earth frame the flight time of light is 2 million years; the flight time of the ship is approximately one part in $10^{11}$ longer. Thus the arrival time of the ship is one part in $10^{11}$ of 2 million years after the light - about ten minutes. The Doppler analysis invokes ticks of the shipboard clock, which I'm not doing.

To illuminate the difference: The Doppler computation results in how much faster the clock on the ships looks to be running. The result of this includes the time dilation of the rocket. The Doppler factor tells us the ratio between the elapsed rocket clock time and the observation time - not the ratio between the 2 million year travel in the Earth rest frame and the observation time. The former ratio will be much smaller as time dilation at the quoted speed is significant.

Assuming the travel distance in the given frame to be L = 2 million years, the computation for the arrival time difference is simply L/v - L/c = L(1-v/c)/v.

 

[PeterDonis]

how it could be that we could see an object which is in actual fact traveling slower than c appear to be traveling faster than c. I understand that you're telling me this is the case.

Not necessarily. I'm telling you how it can be the case that you see light signals arriving from the ship in a much shorter time interval than they were emitted (where "time interval" here is in your frame, not the ship's frame). But, as I pointed out in post #48, interpreting that observation as the ship "appearing to be traveling much faster than light" is highly problematic.

 

[PeterDonis]

I think we're calculating different things.

No, we're not. We are both calculating the same invariant: the time interval registered by the observer's clock on Earth between seeing the light signal showing the ship departing Andromeda, and the ship arriving at Earth. I say that interval is 4.47 years. You say it's about a week. We can't both be right.

 

[PeterDonis]

The Doppler analysis invokes ticks of the shipboard clock

Oops, yes, I see where I went wrong. The Doppler factor has to be applied to the shipboard elapsed time, not the Earth elapsed time. Fortunately it's easy to fix that: for $v = 0.99999999999$ we have $\gamma = 1 / \sqrt{1 - v^2} = 223607$. So the shipboard elapsed time is $2000000 / \gamma = 8.94$ years. And dividing that by the Doppler factor $f = 447214$ gives $2 \times 10^{-5}$ years.

As an extra check, we can note that the difference in arrival times at Earth, calculated by your method, is the distance times a factor $(1 / v) - 1$; this factor is, as you say, $10^{-11}$. Multiplying this by $2 \times 10^6$ gives $2 \times 10^{-5}$ years.

Note that this is not even a week; it's $631$ seconds, or about $10.5$ minutes.

 

[Somoth Ergai]

Not necessarily. I'm telling you how it can be the case that you see light signals arriving from the ship in a much shorter time interval than they were emitted (where "time interval" here is in your frame, not the ship's frame). But, as I pointed out in post #48, interpreting that observation as the ship "appearing to be traveling much faster than light" is highly problematic.

Could you please explain how we could see all of the light from the ships journey in a short time frame. in chronological order. and it not have the appearance of traveling faster than light? I'm beginning to wrap my head around the mechanism of the doppler effect. but I don't see how that does not translate to the object appearing to move faster than it actually is moving.

if we observe the ships journey from start to finish and we track it's movement across space, and the time of travel we observe from earth is less than the time it would take light to travel that distance. how is that not faster than light?

I promise i'm not actually trying to be difficult. it just doesn't make sense to me.

 

[pervect]

well that's nice and all but without an explanation of how or why i'm wrong that just sounds like "nuh uh"

You already noted that the light is faster than the ship. Thus, the light should reach the Earth first, followed by the ship. This comes simply from the relation velocity = distance * time, or time = distance / velocity. As of yet, this doesn't even involve relativity.

You can put specific numbers in the formula if you like. It's unclear why you think there is a contradiction here. Really, all we can suggest is that you apply some math, do some calculations, and present your argument a bit more rigorously. "Show your work" would be the short answer.

 

[Ibix]

Note that this is not even a week; it's $631$ seconds, or about $10.5$ minutes.

Yes - as noted above, I initially used 2 billion light years and got a week, which turns out to be 10,080 minutes. 10.5 minutes is the correct figure.

 

[PeterDonis]

Could you please explain how we could see all of the light from the ships journey in a short time frame. in chronological order. and it not have the appearance of traveling faster than light?

What does "appearance of traveling faster than light" mean?

The light signals that you see don't tell you how far away the ship was when they were emitted. So you can't calculate a speed just from the light signals alone. You have to bring in other information. What other information would you use, and why would it lead you to describe what is going on as "appearance of traveling faster than light"?

In other words, as things stand now, nobody has anything to explain, because nobody has shown why "appearance of traveling faster than light" is even a valid description to begin with. We have to have some argument for why that is even a valid description first.

if we observe the ships journey from start to finish and we track it's movement across space

How do you "track its movement across space"? As above, the light you see doesn't have any distance information in it.

the time of travel we observe from earth is less than the time it would take light to travel that distance

But it isn't. It can't be, because the light arrives before the ship. So the ship's time of travel is longer than the light's time of travel.

 

[Vanadium 50]

Have you stopped for two minutes

Interestingly, that's about the time between a message being posted and the OP's reply, and therefore an upper bound on how long he spends thinking about these messages.

Honestly, I would drop relativity completely. The same conceptual "paradox" exists with a fast-moving car beeping its horn every second or someone pitching baseballs out a car.

 

[Orodruin]

Honestly, I would drop relativity completely. The same conceptual "paradox" exists with a fast-moving car beeping its horn every second or someone pitching baseballs out a car.

I did bring up the sound analogy …

 

[Vanadium 50]

I know, but I suggest we get this straight first, before overturning a century of physics.

 

[Bandersnatch]

If you divide 2 million by 4.47 you get a speed which is much faster than . But calling that "traveling much faster than light" is wrong, and even calling it "appearing to travel much faster than light" is highly problematic.

And yet, that's almost verbatim how it's called in astronomy, in the context of AGN jets. Because that's how they look like at a first glance. No need to bash the OP for using the same nomenclature as textbooks do, as long as they leave with an understanding that this is isn't really what it says on the tin.

 

[Somoth Ergai]

How do you "track its movement across space"? As above, the light you see doesn't have any distance information in it.

Doesn't it? I'm sorry I don't understand how that statement could be accurate. the only way we can tell where anything is at all is by measuring the light emitted from it against it's surroundings. How else do we even know how far away the planet is?

Are you saying that objects moving very fast don't have distance information while slower moving objects do? Again, i'm sorry but I'm not understanding your point.

What does "appearance of traveling faster than light" mean?

What I mean is, 1) if we know how far away the planet they are departing from is (2 million light years). and 2) we can determine how far away the back ground stars are. And 3) we can can follow the ship as it makes it's journey. then we should be able to "see" how quickly the light emitted from the traveling ship
"appears" to cross the distance of space and calculate the velocity. I believe this is the same way we determine how quickly anything else is moving in space.

It follows then, necessarily, that 1) a photon crossing that distance (2 million light years) would take two million years from point A (their planet) to point B (Earth). And 2) that if the time it takes the ship to cross that distance, again from our perspective, is less than the time it would have taken a photon to cross that distance then the ship must, as a matter of logical non contradiction, "appear" to cross the distance faster than light.

I believe I am beginning to understand how the doppler effect makes this true, but I'm not fully there yet. however if you're saying that this is not the case then I am still quite lost.

 

[PeterDonis]

that's almost verbatim how it's called in astronomy, in the context of AGN jets.

Yes, I know the terminology is used; I'm just saying that one has to be very careful in interpreting what it means. Scientists often use language to communicate with each other that, for them, is not a problem because they all understand the actual physics and don't get misled--but which can still be very misleading to a lay person who is not aware of all the complications lurking underneath what seems like a simple use of terminology.

 

[PeterDonis]

How else do we even know how far away the planet is?

How do we know how far away the Andromeda galaxy is? Do we know that just by looking at the light coming from that galaxy?

The answer is no, we don't. We have to calculate how far away it is by combining the information in the light we see from it with other information from other sources. In the case of the Andromeda galaxy, we have to measure the periods of Cepheid variable stars we see in that galaxy, and then use a relationship for Cepheid variables between the period and the luminosity, which we have to obtain by observing Cepheid variable stars in our own galaxy, to calculate the luminosity of the Cepheids we see in the Andromeda galaxy. Then we combine that with the apparent brightness of those Cepheids to calculate their distance.

This is the sort of thing I was referring to when I said the light we see, by itself, doesn't tell us distances (or times). So we can't just "track the distance" by looking at the light. We have to already know the distances some other way and then calculate things.

we can determine how far away the back ground stars are

What "background stars" are you talking about? The ship is coming straight from Andromeda to us. The only "background" we are seeing it against is the Andromeda galaxy itself. We certainly don't have "background stars" placed at convenient intervals all along the way that send us a signal when the ship passes them.

I don't think you have thought through very carefully what we would actually be observing in the scenario you have described.

a photon crossing that distance (2 million light years) would take two million years from point A (their planet) to point B (Earth)

In the Earth's rest frame, yes. But note that this statement is only true in the Earth's rest frame.

the time it takes the ship to cross that distance, again from our perspective, is less than the time it would have taken a photon to cross that distance

But it isn't. You have already been told this, repeatedly. But let me restate it again.

Call the time in the Earth's frame when the ship leaves Andromeda time zero. A light signal is emitted from the ship towards Earth at the same instant.

That light signal arrives at Earth at time 2 million years.

The ship itself arrives at Earth at time 2 million years plus about 10.5 minutes (per the calculations done in earlier posts).

In other words, the ship arrives after the light. So it can't possibly take less time than the light takes to travel the same distance. If it did, the ship would arrive before the light, not after it.

Now let's talk about the "speed much faster than light" calculation. How is that calculated? It's calculated by taking the distance of 2 million years and dividing it by 10.5 minutes, i.e., the time elapsed on Earth between the light arriving and the ship arriving. But this same calculation would say that the light itself travels with infinite speed, since the time between the light arriving and the light arriving is, well, zero. So here again the ship does not travel faster than the light does. It travels faster than $c$ by this calculation, but the light travels faster than $c$ too--in fact infinitely faster. This is why I say that describing this as "the ship appearing to travel much faster than light" is misleading--because you would then have to describe the light itself as traveling infinitely faster than light.

 

[Dale]

It follows then, necessarily, that 1) a photon crossing that distance (2 million light years) would take two million years from point A (their planet) to point B (Earth). And 2) that if the time it takes the ship to cross that distance, again from our perspective, is less than the time it would have taken a photon to cross that distance then the ship must, as a matter of logical non contradiction, "appear" to cross the distance faster than light.

You said “that distance” 3 times and “the distance” once. In this problem there is no one unique distance. There are varying distances ranging from 2 million light years to 0. There is light that travels all of those varying distances. I think a big part of the problem is that you are fixated on a single distance in a problem whose distance varies.

 

[Chicken Squirr-El]

Take a look at these spacetime diagrams of the twin paradox from wikipedia:
https://upload.wikimedia.org/wikipedia/commons/a/a2/Rstd4.gif

The top half of the right image is the ship traveling towards you in your frame of reference. The bunched up blue lines at the top are what you see through your telescope from launch to arrival and demonstrates why you see all the light signals of the entire trip during a short interval at the very end.

 

[Somoth Ergai]

Take a look at these spacetime diagrams of the twin paradox from wikipedia:
https://upload.wikimedia.org/wikipedia/commons/a/a2/Rstd4.gif

View attachment 342496

The top half of the right image is the ship traveling towards you in your frame of reference. The bunched up blue lines at the top are what you see through your telescope from launch to arrival and demonstrates why you see all the light signals of the entire trip during a short interval at the very end.

yes I think i have started to understand. And please point out where, if at all, I'm going wrong. But here's how I think I understand it. Because of the speed of the ship and the doppler effect, the light from the ship will arrive sort of "squashed together" such that from our reference frame the ship will appear to complete its journey from start to finish in a kind of fast forward. The point of confusion for me now is that another user says if i'm understanding him correctly, this does not mean the ship will appear to move from point a to point b faster than light.

I'm struggling with this because it seems contradictory. if we imagine observing an object travel from an arbitrary point A to an arbitrary point B and say that distance is 100 miles. and we observe that the object travels at 100 miles per hour. I would expect the object to take one hour to complete it's journey.

All good

If we speed things up and increase the distance. say, 2 million light years and the object travels at near light speed my intuition was telling me that the observed journey should take nearly 2 million years. I think I now understand how and why this is not the case due to the doppler effect. which, according to the experts, means that the observed journey will take about 10 minutes.

Still good. I thought.

where I'm stuck now is that my intuition tells me that if an object on a 2 million year journey appears to complete its trip over the course of 10 minutes that it must have an apparent motion faster than light.

Which makes sense because all of the light from the trip arrives closer together than it would have if the ships actual speed was much slower. but, as I said, I'm being told this interpretation is wrong also.

 

[PeterDonis]

Because of the speed of the ship and the doppler effect, the light from the ship will arrive sort of "squashed together" such that from our reference frame the ship will appear to complete its journey from start to finish in a kind of fast forward.

Yes.

The point of confusion for me now is that another user says if i'm understanding him correctly, this does not mean the ship will appear to move from point a to point b faster than light.

More precisely: I am saying that if you interpret what you describe above as "the ship appears to move faster than light", then you must also say that the light itself appears to move "faster than light"--indeed, infinitely fast.

So it's your choice: either you can adopt the "appears to travel faster than light" interpretation completely, with the implication I just stated for the speed of light itself, or you can refuse to adopt the "appears to travel faster than light" interpretation at all, so that you don't have to accept the necessary implication that light itself appears to be traveling infinitely fast.

My personal preference is for the second choice.

 

[PeterDonis]

My personal preference is for the second choice.

I called this a "personal preference", but perhaps I should expand on this.

If you interpret "squashing together" of the light due to the relativistic Doppler effect as "the ship appears to travel faster than light", you are assuming that the light itself takes no time to travel to you--in other words, you are assuming that the "squashing together" observation is only telling you about the ship's travel, not about the light's travel. But of course the light doesn't actually take zero time to travel to you. So you can't actually ignore the travel time of the light when you are trying to interpret the "squashing together" of the light that you see.

And that means that what you see is not just telling you about the ship's travel. It is telling you about both the ship's travel and the light's travel, and in order to conclude anything about the ship's travel alone from what you see, you have to figure out how to separate out the two effects--the ship's travel and the light's travel--in what you see. But the light you see, in itself, can't tell you how to do that. You have to use other information.

And the most obvious other information to use is that you know that the ship's launch point is 2 million light years away, so the light from the launch takes 2 million years to get to you, and the ship itself takes 10.5 minutes longer than that. So in the course of the trip, the light travel time from the ship to you changes from 2 million years to zero. So it makes sense to interpret almost all of the "squashing" of the light that you see as being due to the change in the light's travel time, instead of being due to any weirdness in what the ship is doing.

 

[Orodruin]

It travels faster than $c$ by this calculation, but the light travels faster than $c$ too--in fact infinitely faster. This is why I say that describing this as "the ship appearing to travel much faster than light" is misleading--because you would then have to describe the light itself as traveling infinitely faster than light.

By the same argument, let’s say that I manage to arrive at the end of a 100 m dash 5 s after Usain Bolt. This does not mean I ran faster than Usain Bolt just because our arrival time difference was shorter than it took Usain to complete the race.

 

[Somoth Ergai]

I called this a "personal preference", but perhaps I should expand on this.

If you interpret "squashing together" of the light due to the relativistic Doppler effect as "the ship appears to travel faster than light", you are assuming that the light itself takes no time to travel to you--in other words, you are assuming that the "squashing together" observation is only telling you about the ship's travel, not about the light's travel. But of course the light doesn't actually take zero time to travel to you. So you can't actually ignore the travel time of the light when you are trying to interpret the "squashing together" of the light that you see.

And that means that what you see is not just telling you about the ship's travel. It is telling you about both the ship's travel and the light's travel, and in order to conclude anything about the ship's travel alone from what you see, you have to figure out how to separate out the two effects--the ship's travel and the light's travel--in what you see. But the light you see, in itself, can't tell you how to do that. You have to use other information.

And the most obvious other information to use is that you know that the ship's launch point is 2 million light years away, so the light from the launch takes 2 million years to get to you, and the ship itself takes 10.5 minutes longer than that. So in the course of the trip, the light travel time from the ship to you changes from 2 million years to zero. So it makes sense to interpret almost all of the "squashing" of the light that you see as being due to the change in the light's travel time, instead of being due to any weirdness in what the ship is doing.

I think I get it now. And I apologize if my language is not as precise as you would like. I am actually trying to get this right. Here's how I understand it.

First Let's get rid of the ship altogether. suppose we're observing through our telescope and one of the aliens points a flashlight directly at us. A miracle of aim I know. they flick the flashlight on and then off. we would see the light emitted from the flashlight right away. we know several things form this event. if we imagine being able to watch one of the emitted photons leave the flashlight and follow it to earth, the apparent travel time would be zero. As you said, the light would appear to travel infinitely fast.

it would have to in order for us to see the flashlight turn on. And in fact, this would seem to be true for all of the light being emitted by the entire planet. or anything else for that matter. at every interval of time there are new photons being cast our way and if we had some magical ability to watch any one of them they would all appear to get from their point of origin to our eyeballs instantaneously.

I feel i should pause here and ask if I've gone horribly wrong in my understanding again but this genuinely seems to be the implication of what you have been saying.

If i do understand correctly, then going back to the ship it too will appear to move faster than it's actual velocity because as it moves toward us it bunches up all the photons which then arrive closer together. reflecting a sped up time frame that is different from the actual "physical" time the ship spent in transit.

Which also, as you pointed out, means that the light does in fact appear to travel faster than itself. I understand now that this is an illusion caused by the bunching up of the photons. I would go further to say that being that the light we see from the ship does not reflect the actual position of the ship at the time of observation, the entire thing is a kind of optical illusion.

Please let me know if I have gone terribly wrong in my understanding again.

 

[Dale]

this does not mean the ship will appear to move from point a to point b faster than light

The ship can not move from point a to point b faster than light. This is constrained by the laws of physics.

The ship can “appear” to move from point a to point b faster than $c$, with “appear” defined as you described above. Nothing in the laws of physics constrains this. In fact, with that definition of “appear”, light itself "appears" to move infinitely fast. So while the spaceship does “appear” to move faster than $c$, it does not “appear” to move faster than light.

 

[Dale]

as you pointed out, means that the light does in fact appear to travel faster than itself

The correct statement would be: light “appears” to travel faster than $c$. $c$ is the speed that light moves in an inertial frame. It is not the speed that light “appears” to travel.

I would go further to say that being that the light we see from the ship does not reflect the actual position of the ship at the time of observation, the entire thing is a kind of optical illusion.

Yes. The relativistic effects of time dilation, length contraction, and the relativity of simultaneity are what remain after correcting for this optical illusion.

 

[PeterDonis]

they flick the flashlight on and then off. we would see the light emitted from the flashlight right away.

No, we don't. If the alien is 2 million light years from us when they flick the flashlight on, we see the light 2 million years (according to our rest frame) after it is emitted.

if we imagine being able to watch one of the emitted photons leave the flashlight and follow it to earth, the apparent travel time would be zero.

The "apparent travel time" in our rest frame is not zero. See above.

It is correct that the arc length along the light ray's worldline would be zero, but you cannot interpret that as a "travel time".

The "apparent travel time" according to a different interpretation than the one using our rest frame can give this answer, but only for one light ray, the first one the aliens emit. See below.

As you said, the light would appear to travel infinitely fast.

One particular ray of light would appear to if you adopt a particular interpretation, where you take the first light ray emitted by the alien as a "baseline", and calculate a "speed" for any object that arrives at your location by dividing the distance by the time elapsed on your clock between receiving the "baseline" light ray and the object arriving. So the "baseline" light ray would travel at infinite speed by this interpretation (since it arrives at the same time as itself). But other light rays you receive later than the "baseline" light ray would not. (Note that this is an implication that I did not state in my previous post, but it should be obvious if you read my previous post carefully and think about how the ship's speed is calculated. Any light ray arriving later than the "baseline" is treated like the ship.)

What you said above does not take into account these critical factors. Furthermore, one of the reasons I went into all that detail to describe the implications of this interpretation is to get you to think critically about whether it really makes sense to calculate a speed this way. I would suggest going back and thinking about that again in the light of what I've said above.

it would have to in order for us to see the flashlight turn on. And in fact, this would seem to be true for all of the light being emitted by the entire planet. or anything else for that matter. at every interval of time there are new photons being cast our way and if we had some magical ability to watch any one of them they would all appear to get from their point of origin to our eyeballs instantaneously.

No. See above.

I feel i should pause here and ask if I've gone horribly wrong in my understanding

In some ways, you have. See above.

If i do understand correctly, then going back to the ship it too will appear to move faster than it's actual velocity because as it moves toward us it bunches up all the photons which then arrive closer together. reflecting a sped up time frame that is different from the actual "physical" time the ship spent in transit.

You can adopt an interpretation that works this way, but it does not have the implication that all light rays travel infinitely fast. See above.

Which also, as you pointed out, means that the light does in fact appear to travel faster than itself.

Sort of. See above.

I understand now that this is an illusion caused by the bunching up of the photons.

You can think of it that way, yes.

I would go further to say that being that the light we see from the ship does not reflect the actual position of the ship at the time of observation

As I have already pointed out, the light we see from the ship does not tell us anything about "position" by itself. It doesn't reflect the ship's actual position, but it doesn't reflect any other position either.

the entire thing is a kind of optical illusion.

You can think of it that way, yes.

 

[ersmith]

Another way to think about it is that if we see the ship's launch before the ship arrives, then by definition the ship is moving slower than light (because the light from the launch got here before the ship did).

In order for the ship to be moving faster than light, we would have to see its launch *after* the ship has already arrived.

 

[Bombu]

If the people on the spaceship celebrated Christmas every year by lighting up their Christmas tree then isn't it correct that all observers would count same number of Christmas tree lightings (or flashes), in this example almost 2 million? From the spaceship's perspective the flashes would occur once a year. How often would the flashes appear in OP's telescope? (Also, as I've learned thanks to this forum, in an expanding universe,
the light from 2 million light years away would take more than 2 million years to get here, but I imagine that can be neglected for the purposes of this discussion).

 

[PeterDonis]

If the people on the spaceship celebrated Christmas every year by lighting up their Christmas tree then isn't it correct that all observers would count same number of Christmas tree lightings (or flashes)

Yes.

in this example almost 2 million?

No. On the spaceship less than 9 years elapse during the trip.

in an expanding universe

Which doesn't apply here as our galaxy and the Andromeda galaxy are part of the same gravitationally bound group, the Local Group, so their relative motion is not affected by the expansion of the universe.

 

[Bombu]

Ok, I guess I'd better butt out before people start being mean to me.

I suppose the photons don't experience any time but I don't see how they can also have a frequency.

I thought I'd read years ago that ultimately the expansion would separate all matter so that atoms couldn't exist.

But, I don't want to hijack the thread. Thanks for your response.

 

[PeterDonis]

I suppose the photons don't experience any time

No, that's not correct. What is correct, as I said in a previous post (not in response to you) is that the arc length along the worldline of a photon (or more correctly a "light pulse", since "photon" is a quantum concept and we're in the relativity forum here) is zero. But you cannot interpret that arc length as "elapsed time". That interpretation only works for timelike worldlines, not lightlike ones.

I thought I'd read years ago that ultimately the expansion would separate all matter so that atoms couldn't exist.

This is only true for a "Big Rip" scenario, which is speculative and for which we have no evidence.

 

[Nugatory]

Ok, I guess I'd better butt out before people start being mean to me.

You're doing fine... We're only mean to people who argumentatively double down on their misunderstandings.

I suppose the photons don't experience any time but I don't see how they can also have a frequency.

It's more that a photon isn't something that can experience time or anything else either. We can observe them, we can measure and describe their behavior, we can talk about where and when they're emitted and where and when they're detected, we can do all of this without assuming that they're experiencing anything. It's really not that different from the rock in my front yard, whose physics I can describe in great detail without ever using the words "it experiences".

I thought I'd read years ago that ultimately the expansion would separate all matter so that atoms couldn't exist.

You probably did, lots of people have said that, they're not exactly wrong, but they are leaving out one important qualification: Expansion will pull two things apart unless there happens to be some stronger force holding them together. For an analogy you could imagine tossing two corks into a turbulent river: they'll both go with the flow, and currents flowing in different directions will tend to pull them apart. But if they're tied together with a string they'll never be separated by more than the length of the string no matter how the currents tug at them.

 

[Somoth Ergai]

No, we don't. If the alien is 2 million light years from us when they flick the flashlight on, we see the light 2 million years (according to our rest frame) after it is emitted.

I'm confused then. If we are observing the alien on the planet, and it points a flashlight at us and flicks it on. We would see the light turn on wouldn't we? Meaning the time from the flashlight turning on and the photon being emitted,to the time we see that photon, would be zero. Again I'm speaking purely from our perspective on earth. I understand that the actual time it took the photon to get here is 2 million years. what I'm saying is purely from what we are visually able to see through our telescope and how things appear to be.

One particular ray of light would appear to if you adopt a particular interpretation, where you take the first light ray emitted by the alien as a "baseline", and calculate a "speed" for any object that arrives at your location by dividing the distance by the time elapsed on your clock between receiving the "baseline" light ray and the object arriving. So the "baseline" light ray would travel at infinite speed by this interpretation (since it arrives at the same time as itself). But other light rays you receive later than the "baseline" light ray would not. (Note that this is an implication that I did not state in my previous post, but it should be obvious if you read my previous post carefully and think about how the ship's speed is calculated. Any light ray arriving later than the "baseline" is treated like the ship.)

I promise I am trying to think this through. It seems like you're saying that my description of seeing the light move instantly from the flashlight to us here on earth is correct but only for the first ray. I may not be understanding the terminology correctly but isn't a single "light ray" the same thing as a photon?

I know I must be misinterpreting you because it seems like that would imply that one photon would appear to be infinitely fast while all other photons would not be.

one of the reasons I went into all that detail to describe the implications of this interpretation is to get you to think critically about whether it really makes sense to calculate a speed this way. I would suggest going back and thinking about that again in the light of what I've said above.

It does make sense to me. Granted, as I think we can agree, what makes sense to me often turns out to be wrong.

Another way to think about it is that if we see the ship's launch before the ship arrives, then by definition the ship is moving slower than light (because the light from the launch got here before the ship did).

In order for the ship to be moving faster than light, we would have to see its launch *after* the ship has already arrived.

I Understand that the actual physical movement of the ship and the light their "real time position in space is more or less independent of what we actually observe. that's the entire point i seem to be confused about. What would we actually see while observing all of this? And by extension what are the implications of what we would actually see? I thought I had it figured out But as you can see I'm still struggling

 

[Orodruin]

I'm confused then. If we are observing the alien on the planet, and it points a flashlight at us and flicks it on. We would see the light turn on wouldn't we? Meaning the time from the flashlight turning on and the photon being emitted,to the time we see that photon, would be zero. Again I'm speaking purely from our perspective on earth. I understand that the actual time it took the photon to get here is 2 million years. what I'm saying is purely from what we are visually able to see through our telescope and how things appear to be.

You shoumd stop trying to take this perspective. It is only confusing you. What we typically talk about in relativity is not whag you visually see. It is ehat remains of what you visually see once the light travel time has been accounted for and the delay taken out. You see the alien flick the light and you know it happened 2 million years ago because they are 2 million ly away. That’s it.

I promise I am trying to think this through. It seems like you're saying that my description of seeing the light move instantly from the flashlight to us here on earth is correct but only for the first ray. I may not be understanding the terminology correctly but isn't a single "light ray" the same thing as a photon?

This is classical physics. You should not try to think about photons, which in many respects is one of the absolutely least classical things you can encounter. We know people use it colloquially as ”a small ball of light” many times in relativity discussions, but it isn’t and should be avoided. ”Light pulse” will do perfectly fine in most situations.

And by extension what are the implications of what we would actually see?

Nothing. Not until you account for travel time and correct for it.

 

[Orodruin]

To add a bit to that: It is possible to write down relativity in coordinates that provide a simultaneity convention that agrees with what you are attempting. You end up with a coordinate speed of light that is indeed infinite in one direction and c/2 in the other. The reason we do not use such coordinates is that it would generally be a lot messier. Instead we use the Einstein synchronization convention, in which we correct for light travel time and assume the one-way speed of light in any direction is equal to the two-way speed of light c.

 

[PeroK]

I Understand that the actual physical movement of the ship and the light their "real time position in space is more or less independent of what we actually observe. that's the entire point i seem to be confused about. What would we actually see while observing all of this? And by extension what are the implications of what we would actually see? I thought I had it figured out But as you can see I'm still struggling

You said in your introductory post that you watch a lot of science videos. One of the issues with popular science videos on relativity is that they over-emphasise the role of light and the "observer". That is precisely what you are doing. Phrases like "perspective" and "vantage point" point indicate that you have been led astray by these videos to believe that relativity has a subjectivity to it. That subjectivity, however, is not inherent in the actual physics.

 

[Dale]

We would see the light turn on wouldn't we? Meaning the time from the flashlight turning on and the photon being emitted,to the time we see that photon, would be zero.

No. The time from the flash being emitted to the time you see that flash is the distance it traveled divided by $c$. This rule always applies for all light in any inertial frame.

Again I'm speaking purely from our perspective on earth. I understand that the actual time it took the photon to get here is 2 million years. what I'm saying is purely from what we are visually able to see through our telescope and how things appear to be.

The time between when the light flash arrives and when it “appears” to leave is zero. This is basically just a tautology since in your OP you describe “appears” as meaning when the light from something arrives. So it is just saying that the light from the flash arrives when the light from the flash arrives. Which is tautologically true.

It seems like you're saying that my description of seeing the light move instantly from the flashlight to us here on earth is correct but only for the first ray.

The statement “the light moves instantly from the flashlight to us here on earth” is wrong. This is wrong for all rays.

The statement you want to make is “the light arrives at the instant it ‘appears’ to leave”. This is tautologically true for all rays based on your meaning of “appears”.

One of the problems that you are running into is that you are focusing on this concept of “appears” that is simply not a big part of relativity. We essentially assume that all observers correct for appearances and we talk about what is happening instead of what “appears” to happen. This problem is compounded by your inconsistent usage of the term in your own writing. Sometimes you say something happens when you mean that it “appears” to happen. I think you will resolve a lot of your own confusion if you carefully use the word “appears” when you are talking about appearances and don’t use it when you are talking about what is happening.

 

[hutchphd]

Meaning the time from the flashlight turning on and the photon being emitted,to the time we see that photon, would be zero.

I Understand that the actual physical movement of the ship and the light their "real time position in space is more or less independent of what we actually observe.

This is the crux. What do you mean by observe? For a scientific observation, we make our very best estimation (measurement) of an event. It does not necessarilly correspond to what we see with our eyeballs. If someone shows you a ten year old photograph, you will not assume this to be present reality. Scientific observation requires that we correct for any known systematic error. In this case an observation requires us to correct for known finite propagation times for light. This , when done correctly, may be at odds with our your day to day intuition. Too bad......that is confusion, not paradox. Special relativity , insofar as we know, is both correct and self consistent, even though it boggles our poor minds.

 

[PeterDonis]

If we are observing the alien on the planet, and it points a flashlight at us and flicks it on. We would see the light turn on wouldn't we?

Yes, after the light has time to travel to us. If the alien is 2 million light years away, then we see the flashlight go on 2 million years after the alien turns it on.

Meaning the time from the flashlight turning on and the photon being emitted,to the time we see that photon, would be zero.

No. This has already been explained to you more than once.

Again I'm speaking purely from our perspective on earth. I understand that the actual time it took the photon to get here is 2 million years.

The 2 million years is from "our perspective on earth". The "perspective" in which we calculate a speed much faster than $c$ for the ship and an infinite speed for the first light ray we see is not "our perspective on earth". It is not an inertial frame in which earth is at rest. It is something different.

what I'm saying is purely from what we are visually able to see through our telescope and how things appear to be.

No, it isn't. When you see the alien's flashlight turn on, purely from that information alone, you don't know how long it took the light you are seeing to reach you. You can't say "the light took zero time to reach me" just from looking at the light. The light is not telling you that. You have to adopt a particular interpretation of what you are seeing, and we have been trying to explain to you why that particular interpretation is not a good one for you to use.

It seems like you're saying that my description of seeing the light move instantly from the flashlight to us here on earth is correct but only for the first ray.

For the interpretation that calculates a "speed" for the ship that is much faster than $c$, yes, because you are using the time elapsed on your clock between the arrival of the first light ray (the one from the launch of the ship) and the ship. So you would have to apply the same reasoning to other light rays that arrive after the first one--which means their speed is not infinite.

Please note, again, that I am not recommending this interpretation. Indeed, I am trying to show you how confusing it is by pointing out implications of it that astronomers who use it don't normally discuss.

I may not be understanding the terminology correctly but isn't a single "light ray" the same thing as a photon?

No. I already explained this.

What would we actually see while observing all of this?

I already explained that too. See post #68. To restate the "what would we actually see" part of that: we see the light ray emitted when the ship launches from Andromeda. Over the next 10.5 minutes we then see all of the light rays emitted by the ship during its journey, in order. At the end of that 10.5 minutes, the ship arrives.

 

[DAH]

I like to read threads like this one and they seem to get a lot of attention from the regulars here as well. I think the OP is getting confused with the difference between seeing events and observing events. Seeing an event is when the light from that event reaches your eye or telescope in this case, however in special relativity its usually more about observing events in spacetime, and you assign coordinates to when those events actually happened. So in this case, when you see the launch of the ship, the time coordinate would be T minus 2 million years. Then 10 minutes later when the ship arrives on Earth, the time is T = 10 min, so the total travel time as observed from Earth is just over 2 million years.

The seeing events is a totally different thing where you would have to account for a huge Doppler factor and apparent superluminal speeds many times the speed of light.

 

[Somoth Ergai]

I like to read threads like this one and they seem to get a lot of attention from the regulars here as well. I think the OP is getting confused with the difference between seeing events and observing events.

Yes, after the light has time to travel to us. If the alien is 2 million light years away, then we see the flashlight go on 2 million years after the alien turns it on.

This is the crux. What do you mean by observe? For a scientific observation, we make our very best estimation (measurement) of an event. It does not necessarilly correspond to what we see with our eyeballs.

I "see" what you all mean now. and I have in fact been way too sloppy with my terminology. It's even worse than that actually because I know what "observe" means in the context of making measurements. So I should have done better and been more careful with the words I was using. I do apologize for that and I'll try to be better about how I use terms in the future.

In nearly every case where I have used the word "observe" I meant it the way laymen mean it. Probably because I am one myself. as in, if i set up a video camera behind the viewing screen of our telescope and recorded these events and watched it back, what would it look like?

I think a great deal of confusion from both sides of this discussion, admittedly my fault, has been from thinking I meant something different than I did. I believe I do understand the primary errors in my initial post with my failing to understand how the doppler effect would work with this hypothetical recording of the event.

What I have been repeatedly trying and failing to understand now, I think due to my improper use of terms, is indeed what we would see on this video and why.

I already explained that too. See post #68. To restate the "what would we actually see" part of that: we see the light ray emitted when the ship launches from Andromeda. Over the next 10.5 minutes we then see all of the light rays emitted by the ship during its journey, in order. At the end of that 10.5 minutes, the ship arrives.

I appreciate your repeated attempts to explain this and the patience it must take to keep trying still. and I'm sorry I I'm having such a hard time understanding. But, to me, even this explanation is still not answering the primary question I have been trying to get a clear answer to. You said

"Over the next 10.5 minutes we then see all of the light rays emitted by the ship during its journey, in order. At the end of that 10.5 minutes, the ship arrives."

the implication I get from that, is that if we were watching the above described video that 1) we know how far away the planet is (2 million light years). 2) we know that anything traveling at c from that planet to earth will take 2 million years to get from the point of origin to us. and that 3) if we are watching a ship make that same trip in 10 minutes it must "look" like it moved faster than c.

if all of the light rays emitted by the ship (2 million years worth of light information) arrive, one after the other, in the span of 10.5 minutes, then I simply can't understand how it could be the case that the image we see of the trip doesn't appear to be hyper sped up far far beyond c.

Again, I understand that it is not the case that the ship did not, in actual fact, move faster than light at any point along its journey. It is simply due to the doppler effect bunching up all of the light rays so that in effect they arrive all at once which leads to an image that appears to be in fast forward.

the side point I have been trying to grasp, and as others have pointed out appears to be a tautology. Is this. suppose on our hypothetical recording we watch any other normal object, traveling at say, 1000 Mph in a straight line from the alien planet to earth. we are able to watch the object the entire time along its journey. and we will be able to say that the total time of travel (on the recording) the object took X amount of time to get from that point of origin to earth.

Suppose the object is traveling much faster. Say, .99999999999 c. fast enough for the Doppler effect to be significant. The object will still take a certain amount of time to get from point A to Point B. but because of the huge doppler effect the time that it takes will be vastly shorter compared to how fast the physical ship was actually moving.

Meaning that while the "actual" trip took 2 million years and 10.5 minutes. the trip on our recording will only take that 10.5 minutes and thus appear super sped up. giving the appearance of the ship crossing the distance faster than c.

It seems to me that the faster and faster (or more precisely the closer and closer to c) an object moves through space the shorter and shorter it's travel time appears to be on our recording.

Suppose now that the object is a pulse of light coming from a flashlight on this planet 2 million light years away. being that the object is now traveling at c the apparent travel time on our recording should now be zero.

I have tried my very best to avoid using terms in ways I don't mean. I sincerely apologize if i'm still being unclear in what answers i'm actually trying to get. And I appreciate the continued patience everyone has trying to hammer knowledge into me. It's like trying to tattoo a diamond I know. I'm sorry.

 

[PeterDonis]

"Over the next 10.5 minutes we then see all of the light rays emitted by the ship during its journey, in order. At the end of that 10.5 minutes, the ship arrives."

the implication I get from that, is that if we were watching the above described video that 1) we know how far away the planet is (2 million light years). 2) we know that anything traveling at c from that planet to earth will take 2 million years to get from the point of origin to us. and that 3) if we are watching a ship make that same trip in 10 minutes it must "look" like it moved faster than c.

I have already said, multiple times, that this is an interpretation of what you are seeing that you can choose to adopt. You just have to be willing to accept what comes with it.

if all of the light rays emitted by the ship (2 million years worth of light information) arrive, one after the other, in the span of 10.5 minutes, then I simply can't understand how it could be the case that the image we see of the trip doesn't appear to be hyper sped up far far beyond c.

Sure, because you are interpreting "2 million light-years divided by 10.5 minutes" as the apparent speed of the ship. But the "video" you are seeing only gives you the 10.5 minutes (since that's how long it takes you to watch it). It doesn't give you the 2 million light years. You got that from somewhere else, and decided to use it to interpret what you are seeing in the video. You can choose to do that, but nothing forces you to. And, as above, if you do choose to do it, you have to accept what comes with it.

It seems to me that the faster and faster (or more precisely the closer and closer to c) an object moves through space the shorter and shorter it's travel time appears to be on our recording.

Yes.

Suppose now that the object is a pulse of light coming from a flashlight on this planet 2 million light years away. being that the object is now traveling at c the apparent travel time on our recording should now be zero.

Yes.

But note that in the last two statements I quoted, you only made statements about the "apparent travel time", i.e., the time in between the first light ray arriving at your location, and the object itself (which in your second example above is the first light ray) arriving at your location. And those statements are direct observations involving the light you are seeing; you can directly read off the elapsed time on your clock during the "video" (in your second example above that time is zero).

You said nothing at all about "apparent speed" in the above quotes. And you don't have to. Nothing forces you to take the observations you describe and conclude anything about "apparent speed".

If you do want to conclude anything about apparent speed, then, as I have already said, you need to bring in other information that is not directly observable in the light you are seeing, information which gives you a distance, which you then divide by your "apparent time" to obtain an "apparent speed". And you have chosen to do that in a way which makes the object in your first example above have an "apparent speed" much faster than $c$, and the light ray in your second example above have an infinite "apparent speed". And if all that seems ok to you, then sure, go ahead and interpret things that way.

But if it doesn't seem ok to you (and why else would you be belaboring this?), then the only solution to that problem is to stop interpreting things that way. In other words, stop insisting on dividing a distance you obtained some other way by the time it takes you to watch a video of a trip, and calling that the "apparent speed". This isn't something you're going to figure out by asking questions or looking at equations. It's a choice you have to decide to make if you don't like the implications of the alternative.

 

[Tom.G]

Asking Google to define apparent:

ap·par·ent​

/əˈperənt/

adjective
clearly visible or understood; obvious.
"it became apparent that he was talented"

Going back to the flashlight on the distant planet scenario. Two flashes are seen here 10.5 minutes apart.

With no other information, how is the choice made between:
1) the flashlight was turned On and Off two times 10.5 minutes apart
2) the flashlight was turned On and Off once at the distant planet,

then, traveling close to the speed of light, was turned On and Off at 1000 miles from the same observer​

Asking Google to define apparent:

ap·par·ent​

/əˈperənt/

adjective
clearly visible or understood; obvious.
"it became apparent that he was talented"

Much of the discussion about apparent sure looks like differing interpretations of the word between the popular 'common usage' and a different specific interpretation in the astrophysics community. Is it worth anyones time to clearly explain that difference, if any?

Cheers,
Tom

 

[Dale]

I simply can't understand how it could be the case that the image we see of the trip doesn't appear to be hyper sped up far far beyond c.

It does “appear” to be hyper sped up, far far beyond $c$.

It seems to me that the faster and faster (or more precisely the closer and closer to c) an object moves through space the shorter and shorter it's travel time appears to be on our recording.

Yes. (For objects moving towards us)

There is nothing in physics that constrains it to “appear” to travel at less than $c$.

 

[PeroK]

The miracle of the Doppler effect!

 

[Orodruin]

The miracle of the Doppler effect!

... which is also not a necessarily something related to special relativity. Sound exhibits this behaviour too!

... as mentioned many times over ...

 

[PeroK]

... which is also not a necessarily something related to special relativity. Sound exhibits this behaviour too!

And bricks! Before I started university I got a summer job at a brick works. One of the jobs was to stack the "green" bricks onto a pallet to be fired. The bricks would come along a conveyor belt about 3m long. You would walk towards the machine, so the bricks came quicker, then walk back to the far end of the belt and rest your arms for a few seconds before repeating. It certainly seemed less monotonous that way.