Perception of Velocity in Special Relativity

[BadgerBadger92]

TL;DR

How fast is perceived velocity from a different frame of reference in special relativity?

If an object is going close to the speed of light, will outside frames of references perceive the moving object as going slow or fast?

 

[PeterDonis]

If an object is going close to the speed of light

Relative to what? Speed is always relative.

will outside frames of references

What does this even mean?

perceive the moving object as going slow or fast?

It will obviously depend on how whatever is doing the observing is moving relative to the object.

 

[BadgerBadger92]

Relative to what? Speed is always relative.What does this even mean?It will obviously depend on how whatever is doing the observing is moving relative to the object.

Let me clarify

If an object is going close to the speed of light, would people not in the moving frame of reference see the object as going slow?

 

[PeterDonis]

If an object is going close to the speed of light

Relative to what?

would people not in the moving frame of reference see the object as going slow?

Not in what moving frame of reference?

 

[BadgerBadger92]

Relative to what?Not in what moving frame of reference?

“Relative to what?”

Relative to someone not moving

“Not in what moving frame of reference?”

Like someone not moving compared to something close to the speed of light.

 

[PeterDonis]

Relative to someone not moving

There is no such thing. "Moving" and "not moving" are not absolutes. They are relative.

Like someone not moving compared to something close to the speed of light.

Neither of these are absolutes. They are relative. You, right now, are moving at close to the speed of light relative to cosmic ray particles coming into the Earth's atmosphere from space. But you are not moving at all relative to the room you are in. So you can't just say you are "not moving" without qualification; you need to specify relative to what you are not moving.

Similarly, when you ask how someone would see some object moving, obviously the answer is going to depend on how the object is moving relative to the someone. There is no answer to the question without that; and with that, the answer to the question is so obvious that it's pointless to even ask the question.

You need to take a step back and reconsider what you are asking in the light of all of the above.

 

[FactChecker]

“Relative to what?”

Relative to someone not moving

“Not in what moving frame of reference?”

Like someone not moving compared to something close to the speed of light.

If something is going close to the speed of light relative to someone who is "not moving",
Then he is going close to the speed of light relative to someone who is "not moving".

So the set-up of your question, stated more carefully, actually answers the question.

UPDATE: Maybe I misunderstood your question. If person A thinks that person B is moving away at nearly the speed of light, then person B also thinks that person A is moving away at nearly the speed of light. (See @Nugatory 's post below)

 

[Nugatory]

If an object is going close to the speed of light, will outside frames of references perceive the moving object as going slow or fast?

If object A is moving at speed $v$ (which may be close to the speed of light) relative to object B, then…

Using the frame in which A is at rest, the speed of A is zero and the speed of B is $-v$.

Using the frame in which B is at rest, the speed of A is $v$ and the speed of B is zero.

Using a frame in which B is moving at speed $u$, the speed of A is $(u+v)/(1+uv)$, the relativistic velocity addition rule (and using units in which $c=1$).

Whether any of these are “slow or fast” depends on what you’re comparing them with.

 

[malawi_glenn]

Can you define percived velocity

 

[BadgerBadger92]

Can you define percived velocity

How fast something looks like it’s going.

Based on my understanding (and I’m probably wrong) From the viewpoint of the fast moving object, it measures as fast. And from the person watching views it as going slow.

I can’t find an easy way to word it

 

[PeterDonis]

From the viewpoint of the fast moving object, it measures as fast.

No, it measures as not moving at all. Every object is at rest relative to itself.

And from the person watching views it as going slow.

If "the person watching" is a person that the object is moving fast relative to, then they view it as moving fast relative to them. Because moving fast is, you know, moving fast.

 

[PeterDonis]

How fast something looks like it’s going.

This is vague, but the obvious interpretation is how fast something looks like it's moving relative to the observer. Which, as has already been commented several times, is something you put in to your specification of the scenario. You specify that the object is "moving fast" relative to the observer, so of course the observer views it as "moving fast", because you said so.

I can’t find an easy way to word it

If the above is not what you meant, then, again, I think you need to take a step back and think carefully about what you are asking. In particular, what specific observations are you asking about? The only observation described so far is observing speed--how fast some other object is moving relative to the observer. We've already described how that behaves. If you're thinking of some other observation, what is it?

 

[malawi_glenn]

How fast something looks like it’s going.

Based on my understanding (and I’m probably wrong) From the viewpoint of the fast moving object, it measures as fast. And from the person watching views it as going slow.

I can’t find an easy way to word it

what is the difference in seeing how fast it moves than measure how fast it moves?

 

[Ibix]

How fast something looks like it’s going.

Based on my understanding (and I’m probably wrong) From the viewpoint of the fast moving object, it measures as fast. And from the person watching views it as going slow.

I can’t find an easy way to word it

I think you think that there is a state of motion where you can be (in some absolute sense) "travelling close to the speed of light". There is not. There is only "travelling close to the speed of light relative to you (or me, or somebody)". So if you are travelling fast relative to me I will see myself as stationary and you as moving fast, and you will see yourself as stationary and me as moving fast.

In both cases, we will see the other moving slowly in the sense that the other's clocks tick slowly and heart beats go slowly and we walk around the ship (assuming we're in ships) slowly, but we are still travelling at 90%c, or whatever.

 

[Herman Trivilino]

Like someone not moving compared to something close to the speed of light.

There is no way to distinguish between the two. All you can say is that these two objects are moving relative to each other.

 

[malawi_glenn]

@Ibix what if you and me move towards eachother?

 

[Ibix]

@Ibix what if you and me move towards eachother?

Depends what you mean by "perceive" or "see". What we directly see is dominated by the Doppler effect, so we see each other moving more rapidly as we close and more slowly as we separate again. If you correct for the changing distance, though, you calculate that the other person's clocks tick slow regardless of the direction.

(I suspect you know this and are prompting me, and it's a good point.)

 

[BadgerBadger92]

Depends what you mean by "perceive" or "see". What we directly see is dominated by the Doppler effect, so we see each other moving more rapidly as we close and more slowly as we separate again. If you correct for the changing distance, though, you calculate that the other person's clocks tick slow regardless of the direction.

(I suspect you know this and are prompting me, and it's a good point.)

This is how I understand it, but if the moving frame of reference is still perceived as going the speed of light, how could it be possible? (I know it is, I’m just confused here) how could it perceive time as “fast forwarding?”

 

[phinds]

TL;DR Summary: How fast is perceived velocity from a different frame of reference in special relativity?

If an object is going close to the speed of light, will outside frames of references perceive the moving object as going slow or fast?

I empathize with your confusion, but as you have been told numerous times in this thread, you HAVE to realize that motion is relative and "fast" and "slow" are meaningless concepts unless you reference them to something.

EVERYONE always sees themselves as being at rest and their time as normal.

Let's take a somewhat complex scenario that, if you really study it, will, I think, answer your question.

We have Traveler, Mover, and Planet.

In the frame of Planet, Traveler is passing close by in space at a speed of 10% of the speed of light. In the frame of reference of Traveler, he is at rest and Planet is moving away from him at 10% of c. Planet sees the traveler's time as slower than their own time. Traveler sees the time of Planet as being slower than his own. Both Traveler AND Planet see their own time as normal.

Mover is moving off in the opposite direction than that of Traveler at 10% of the speed of light in the frame of reference of Planet. In the frame of Planet, the speed of motion and time of Speeder is identical to that of Traveler, except of course that the directions are opposite.

Now, let's look at Mover and Traveler. Relative to Planet, each are moving at 10% of c but in opposite directions. Relative to Mover, he himself is at rest but Traveler is moving away from him at 20% of c. Likewise, in the frame of reference of Traveler, he himself is at rest and Mover is moving away from him at 20% of c. Each of them sees the time of the other as being slow compared to his own time and each of them see their own time as being normal.

That may have been confusing the first time through, but go through it until you understand it.

For the actual computation of how MUCH slower one sees the other's time, Google "Lorentz Transform" (and see post #8 by @Nugatory)

 

[PeterDonis]

if the moving frame of reference is still perceived as going the speed of light

It's not. No frame can "go at the speed of light".

how could it perceive time as “fast forwarding?”

What do you mean by this? Are you referring to the Doppler effect that @Ibix mentioned? Or to "time dilation" (what you calculate as the object's clock rate after allowing for light travel time)? Or to something else? Please, again, take the time to think through what you are asking. This thread has gone on for 20 posts now without anyone having a good grasp of your actual question.

 

[jbriggs444]

how could it perceive time as “fast forwarding?”

It this what you are really trying to get at? The rate at which time seems to be passing on the object being observed?

As it turns out, time does not behave the way you imagine that it does. Time dilation is symmetric.

Upon first learning about special relativity, we are all told about "time dilation". That time advances more slowly the faster you go. We usually get a mental picture of some absolute time in an absolute rest frame with everyone else having clocks that tick slowly in an absolute sense. That turns out to be something of a "lie to children".

[We may think that we "get it" about the lack of an absolute rest frame when the teacher tells us time after time. But we still stubbornly hold onto the notion of absolute time. That intuition is harder to unlearn. It has its hooks in quite deeply].

The truth is otherwise. Important details are buried in the relativity of simultaneity.

When you try to compare the rates of two clocks that are both moving uniformly, you have a problem. You can compare their readings at the instant they fly past one another. But if you want to compare their readings again later on to figure out their relative rates, they will no longer be next to each other. You will want get their final readings "at the same time" so that you can make a fair comparison. But "at the same time" means that you have to have a standard of simultaneity.

When all of your communications are limited to light speed, there is some ambiguity about simultaneity at a distance.

There is an agreed upon standard for synchronization -- Einstein synchronization. We need not go into details. It involves sending light signals back and forth and using a half way time for the round trip. But it turns out that the resulting synchronization depends crucially on an agreed upon standard for being at rest.

Suppose that you and I each have rest frames (and associated synchronization standards). But we are moving relative to each other.

If I synchronize two of my clocks, one at a start line and one at a finish line and if I use those to measure the rate on your clock as you run from my start line to my finish line, I will measure your clock to be running slow.

If you synchronize two of your clocks, one at a start line and one at a finish line and if you use those to measure the rate on my clock as I run from your start line to your finish line you will measure my clock to be running slow.

There is no absolute truth to which of us is really moving fast and which is really sitting still.
There is no absolute truth to which of us has a clock that is really ticking slow.

 

[malawi_glenn]

Depends what you mean by "perceive" or "see". What we directly see is dominated by the Doppler effect, so we see each other moving more rapidly as we close and more slowly as we separate again. If you correct for the changing distance, though, you calculate that the other person's clocks tick slow regardless of the direction.

(I suspect you know this and are prompting me, and it's a good point.)

I was just after the things you mentioned, heart rate and clock ticks. This is longitudinal doppler effect in a nutshell. Anyway, it was for OPs sake I asked.

@Badger get a decent intro book on relativity, like Morins book. And then study it.

 

[BadgerBadger92]

I know the speed of light is not possible for objects with mass to reach.

Never mind guys. I’ll just ask my old high school physics teacher. He’s kind and accepting of questions and can explain them clearly.

 

[PeterDonis]

I know the speed of light is not possible for objects with mass to reach.

Ok, good.

Never mind guys. I’ll just ask my old high school physics teacher. He’s kind and accepting of questions and can explain them clearly.

You already have multiple good answers in this thread; they're just answers to different questions because we can't figure out which of those questions you are actually asking.

 

[weirdoguy]

I’ll just ask my old high school physics teacher. He’s kind and accepting of questions and can explain them clearly.

People here are also kind and accepting, your questions just don't make sense, and your teacher will tell you the same.

 

[PeterDonis]

I can’t find an easy way to word it

It helps to have a good grasp of the standard terminology of SR. Some highly useful terms to know:

Relative velocity (or relative speed): This is typically something you specify when you describe the scenario you are interested in. For example, you might say some object is moving at 90% of the speed of light relative to some particular observer. The 90% of the speed of light here is the relative speed. (If you specify a direction as well, it's a relative velocity.)

Relativistic Doppler effect: This is what an observer will actually directly observe in light coming from the object, using his eyes or some more sophisticated device that can precisely measure the frequency of light. If you know the relative velocity, you can calculate the relativistic Doppler effect; the effect is usually expressed as a frequency shift, either a blueshift (the observed frequency is higher than the emitted frequency from the object) or a redshift (the observed frequency is lower than the emitted frequency from the object).

Relativistic time dilation: This is a calculation by the observer of how slow the object's clock is ticking compared to the observer's clock. It cannot be directly observed, but it can be calculated from the quantities above.

 

[BadgerBadger92]

People here are also kind and accepting, your questions just don't make sense, and your teacher will tell you the same.

My teacher understood my question.

 

[malawi_glenn]

My teacher understood my question.

I find it very hard to believe that your old teacher had the time to read, understand, and reply you in approximately 25 minutes.

 

[PeterDonis]

My teacher understood my question.

And what was your teacher's answer?

 

[BadgerBadger92]

I find it very hard to believe that your old teacher had the time to read, understand, and reply you in approximately 25 minutes.

He gave me a one sentence response.

I asked him on Facebook. We are friends.