B Special relativity thought: Traveling to the future relative to a particle

[L Drago]

TL;DR Summary

The ether drift was proved wrong by Michelson-Morley experiment. Earlier it was believed that it would slow down by a factor of (1-v²/c²)^(1/2). Now we know ether is wrong. The six atomic clocks in different regions show by same time delay and does not indicate ether drift till date.

I think that we travel to future all the time. As all intertial frame of motion is relative. We are currently travelling at very high speeds with relative to a particle accelerator's particle and time is slowing down for us with relative to the particle. I think so we are also travelling to future also with respect to that particle. We are travelling at multiple speeds at the same time although we are at rest.

 

[Herman Trivilino]

I think that we travel to future all the time.

No. We don't travel from one clock-reading to another. We travel from one location to another, and if we know the distance between the locations, and the time it takes to get from one location to the other, we can calculate our speed. Speed has units of distance divided by units of time. Traveling through time is nonsense, it just means that clock-readings always advance, so that if we read a clock now, and then read it again later, the latter reading will be greater than the former reading. That's not traveling, that's just the passage of time.

We are travelling at multiple speeds at the same time although we are at rest.

No. Being at rest just means the speed is stable at zero. The speed of a person is not a property of that person. It's just a measure of the distance he travels divided by the time he spent traveling. The speed of the person measured in different reference frames may be different, but that's not because of anything the person is doing differently in the different reference frames, it's simply because the reference frames are in motion relative to each other.

 

[L Drago]

No. We don't travel from one clock-reading to another. We travel from one location to another, and if we know the distance between the locations, and the time it takes to get from one location to the other, we can calculate our speed. Speed has units of distance divided by units of time. Traveling through time is nonsense, it just means that clock-readings always advance, so that if we read a clock now, and then read it again later, the latter reading will be greater than the former reading. That's not traveling, that's just the passage of time.

No. Being at rest just means the speed is stable at zero. The speed of a person is not a property of that person. It's just a measure of the distance he travels divided by the time he spent traveling. The speed of the person measured in different reference frames may be different, but that's not because of anything the person is doing differently in the different reference frames, it's simply because the reference frames are in motion relative to each other.

But in different frame of references though we are at rest we travel in multiple speeds.

 

[Ibix]

But in different references though we are at rest we travel in multiple speeds.

The point is that "travelling at speed $v$" is an incomplete sentence. The complete version is "travelling at speed $v$ relative to object X". You can substitute "frame" for "object" if you like. Everything has a single well-defined speed relative to any specified frame or object.

In everyday life, we typically leave out the reference object and say things like "you must not drive faster than 30mph". In that case, we mean "...relative to the surface of the Earth". We can get away with being sloppy in that context because it's widely understood what we mean. We cannot get away with it in relativity, though, because we typically discuss circumstances floating in space, or we are explicitly considering measurements made relative to different objects.

So "[w]e are travelling at multiple speeds at the same time although we are at rest" is missing the point entirely. We have a single well-defined speed with reference to any chosen object or frame, but we can pick many different frames to describe it.

 

[jbriggs444]

I think that we travel to future all the time. As all intertial frame of motion is relative. We are currently travelling at very high speeds with relative to a particle accelerator's particle and time is slowing down for us with relative to the particle. I think so we are also travelling to future also with respect to that particle. We are travelling at multiple speeds at the same time although we are at rest.

You have made a number of posts along these lines, making statements in isolation. Giving no indication that you have understood any of them. And then asking whether you have understood correctly.

It seems that you need to learn about coordinate systems and frames of reference.

I like to think about coordinate systems by pretending that we have a transparent plastic sheet that we have placed over a table. There are grid lines on the sheet (for a cartesian coordinate system). We can identify any point on the table by the pair of grid lines that intersect at that point. Those are the coordinates of the point.

If we change out plastic sheets, we have not affected the table. But the points on the table all have new coordinates.

If a point is moving, we can record its motion as a series of coordinate values and calculate how rapidly those coordinates are changing.

If a plastic sheet is moving, we can still record the motion of a point as a series of coordinate values and calculate how rapidly the coordinates are changing.

The same point will have different speeds depending on how fast we drag a plastic sheet over it.

 

[Dale]

I think that we travel to future all the time. As all intertial frame of motion is relative. We are currently travelling at very high speeds with relative to a particle accelerator's particle and time is slowing down for us with relative to the particle.

Yes. I agree.

But in different frame of references though we are at rest we travel in multiple speeds.

This is poorly worded. This would be better: “in different frames of reference we travel at different speeds, though we are at rest in one frame”.

If we are inertial then there is no frame in which we travel at multiple speeds. We travel at different speeds in different frames, but not multiple speeds in any one frame.

 

[L Drago]

Yes. I agree.

This is poorly worded. This would be better: “in different frames of reference we travel at different speeds, though we are at rest in one frame”.

If we are inertial then there is no frame in which we travel at multiple speeds. We travel at different speeds in different frames, but not multiple speeds in any one frame.

Thanks a lot for correcting me

 

[Herman Trivilino]

But in different frame of references though we are at rest we travel in multiple speeds.

In each frame of reference our speed is different. But in only one of those frames our speed is zero. There is no reason to give any special preference to the one in which we're at rest. You seem to do that when you say "though we are at rest" You could just as easily replace it with the phrase "though we have a speed of 12.82 m/s".

 

[Ibix]

A mathematical analogy. Imagine four people sitting around a square table and an ant walking across the table at 1mm/s relative to the table. One person sees the ant moving left-to-right and says the ant has velocity $(+1,0)$. The person opposite them says the ant is moving right-to-left so it has velocity $(-1,0)$. The people sitting between them say the ant has velocity $(0,+1)$ and $(0,-1)$. Does the ant really have four different velocities?

No it does not. It has one velocity - it is doing what it is doing in reality. If we're hoping to describe that reality there had better be only one velocity in our models.

What we do have is four different representations of that velocity, because our four people are using four different coordinate systems whose x and y directions are rotated with respect to one another. This means that "the ant has velocity $(v_x,v_y)$" is meaningless unless you also specify which directions you are considering to be "increasing x while leaving y constant" and "increasing y while leaving x constant".

Note that in all these cases the ant has the same speed, just in different directions. That is because, while the reference frames do not share a notion of x and y directions, they do share a notion of what "at rest" means - it means at rest with respect to the table. Once you add in the possibility of frames which do not consider the table to be at rest, the speed will not be equal in all representations either.

 

[Dale]

No it does not. It has one velocity - it is doing what it is doing in reality.

It is important to point out, in support of this statement, that there is a definition of velocity that is frame-invariant. It does not depend on the reference frame chosen. Strictly speaking, it is the components of that velocity that are coordinate-dependent. But the velocity itself is a geometric quantity that exists independent of any coordinate chart.

 

[pervect]

The whole "time is slowing down" idea is a robust popularization that is unfortunately, incomplete and can be misleading. It's easy to point out that what's missing from the concept is the idea of relativity of simultaneity, but the usefulness of that observation is unfortunately questionable. One of the e issue here is language difficulties. A related issue is that just giving a name to a missing concept does not teach it.

I think the language barriers here may be too large for a good conversation, but I will venture to say that differential aging (as meant by physicists) is a more precise way of talking about the concepts that I suspect the OP is trying to understand.

If two particles or objects (represented mathematically by worldlines) start out at the same event (same location at the same time), and take different paths through space-time to meet again at another event, when they meet up again, the principle of differential aging says that the elapsed times measured on their clocks will in general be different.

Language here, again. The sort of time that is being talked about here is the sort of time a clock keeps, a sort of time called "proper time". This does not include any concepts of past, future, or causality, which is a separate problem, it simply describes how clocks behave.

The (slightly oversimplified) principle of Maximal aging is a refinement on the principle of differential aging. It says that in special relativity (the simplified version doesn't work for the curved space-times of General relativity), the particle with the most elapsed time on it's clock will be the particle that is in inertial motion, one that never accelerated so it is at rest in an inertial frame.

E.F. Taylor wrote a lot about this, but unfortunately I don't have specific references to quote.

 

[Herman Trivilino]

It may be helpful to note that time dilation is symmetrical, each traveler will observe the other's clock dilated compared to their own proper time. Which seems paradoxical until you take the relativity of simultaneity into account. But time dilation is a comparison of a proper time to a dilated time.

But what has come to be called "differential aging" in this forum is actually a comparison of two proper times. The observers will agree on the difference in proper time.

In the parlance of physics, proper time is a relativistic invariant, meaning all observers will agree on its value. Dilated time is not a relativistic invariant, meaning different observers may disagree on its value.

 

[L Drago]

A mathematical analogy. Imagine four people sitting around a square table and an ant walking across the table at 1mm/s relative to the table. One person sees the ant moving left-to-right and says the ant has velocity $(+1,0)$. The person opposite them says the ant is moving right-to-left so it has velocity $(-1,0)$. The people sitting between them say the ant has velocity $(0,+1)$ and $(0,-1)$. Does the ant really have four different velocities?

No it does not. It has one velocity - it is doing what it is doing in reality. If we're hoping to describe that reality there had better be only one velocity in our models.

What we do have is four different representations of that velocity, because our four people are using four different coordinate systems whose x and y directions are rotated with respect to one another. This means that "the ant has velocity $(v_x,v_y)$" is meaningless unless you also specify which directions you are considering to be "increasing x while leaving y constant" and "increasing y while leaving x constant".

Note that in all these cases the ant has the same speed, just in different directions. That is because, while the reference frames do not share a notion of x and y directions, they do share a notion of what "at rest" means - it means at rest with respect to the table. Once you add in the possibility of frames which do not consider the table to be at rest, the speed will not be equal in all representations either.

Suppose I am sitting now and a particle accelerator is besides me particles are travelling in very high speed near light speeds so with relative to the particle I am also travelling in near light speeds. But with respect to the floor ,I am at rest. And with respect to a particle coming in West direction I am travelling in the opposite direction that is east with respect to that particle that means the directions and velocity are all relative. All inertial frame of motion is relative. Am I right ?

 

[Ibix]

Yes

 

[FRANKENSTEIN54]

The whole "time is slowing down" idea is a robust popularization that is unfortunately, incomplete and can be misleading. It's easy to point out that what's missing from the concept is the idea of relativity of simultaneity, but the usefulness of that observation is unfortunately questionable. One of the e issue here is language difficulties. A related issue is that just giving a name to a missing concept does not teach it.

I think the language barriers here may be too large for a good conversation, but I will venture to say that differential aging (as meant by physicists) is a more precise way of talking about the concepts that I suspect the OP is trying to understand.

If two particles or objects (represented mathematically by worldlines) start out at the same event (same location at the same time), and take different paths through space-time to meet again at another event, when they meet up again, the principle of differential aging says that the elapsed times measured on their clocks will in general be different.

Language here, again. The sort of time that is being talked about here is the sort of time a clock keeps, a sort of time called "proper time". This does not include any concepts of past, future, or causality, which is a separate problem, it simply describes how clocks behave.

The (slightly oversimplified) principle of Maximal aging is a refinement on the principle of differential aging. It says that in special relativity (the simplified version doesn't work for the curved space-times of General relativity), the particle with the most elapsed time on it's clock will be the particle that is in inertial motion, one that never accelerated so it is at rest in an inertial frame.

E.F. Taylor wrote a lot about this, but unfortunately I don't have specific references to quote.

I think the simple explanation is >>>>>>>>>>>>>
You said , "
If two particles or objects (represented mathematically by worldlines) start out at the same event (same location at the same time), and take different paths through space-time to meet again at another event, when they meet up again, the principle of differential aging says that the elapsed times measured on their clocks will in general be different."
I would say , the object taking the shorter Distance even travelling at a slower speed than the other object , can arrive at the destination Sooner . Thus its Clock shows Less "ticks" elapsed . But also , the object taking a longer Distance could arrive at the destination Sooner if it travels at a higher rate of speed . And thus its Clock will show Less "ticks" elapsed . So "Time" showing on a Clock , just depends on Distance travelled & Speed while travelling . The object that gets there the quickest , Less time will have elapsed ! That's all !
So , Clocks could be "slower" / showing less Time , whether you are moving slow or moving fast .

 

[Dale]

I would say , the object taking the shorter Distance even travelling at a slower speed than the other object , can arrive at the destination Sooner . Thus its Clock shows Less "ticks" elapsed .

The word "sooner" refers to an ordering. But proper times only provide an ordering on a single worldline. Proper times do not provide ordering between two worldlines.

 

[FRANKENSTEIN54]

The word "sooner" refers to an ordering. But proper times only provide an ordering on a single worldline. Proper times do not provide ordering between two worldlines.

By "sooner" , in my context , I mean its clock can show less ticks elapsed than the clock on the other object , even though the other object may be travelling at a faster speed .

 

[jbriggs444]

By "sooner" , in my context , I mean its clock can show less ticks elapsed than the clock on the other object , even though the other object may be travelling at a faster speed .

"Speed" is a measure that depends upon a choice of coordinates. "Faster speed" has no invariant meaning.

If we settle upon inertial coordinates in which the starting and ending events have identical spatial locations in a flat space time then the [suitably integrated] frame-relative speed figures directly into the cumulative elapsed proper times along the two trajectories.$$\Delta t_\text{proper} = \int_\text{start}^\text{end} \frac{dt}{\gamma(v(t))}$$

 

[Dale]

By "sooner" , in my context , I mean its clock can show less ticks elapsed than the clock on the other object , even though the other object may be travelling at a faster speed .

Yeah, that isn't what the word "sooner" means. If I show up to a meeting with my boss 10 min late, but my watch is set 15 min late, then my boss doesn't agree that I arrived 5 minutes sooner than he did. He was there waiting impatiently for 10 min and knows I didn't arrive sooner.

When words have multiple accepted meanings, it is fine to say "I am using this accepted meaning". It is not acceptable to say "I am just going to use a standard word in a completely different and nonsensical way because I feel like it".

 

[Nugatory]

I would say , the object taking the shorter Distance even travelling at a slower speed than the other object , can arrive at the destination Sooner . Thus its Clock shows Less "ticks" elapsed . But also , the object taking a longer Distance could arrive at the destination Sooner if it travels at a higher rate of speed . And thus its Clock will show Less "ticks" elapsed . So "Time" showing on a Clock , just depends on Distance travelled & Speed while travelling . The object that gets there the quickest , Less time will have elapsed ! That's all !

If you try sketching out a simple Minkowski diagram showing the worldlines of the two objects you will quickly see that this explanation cannot be correct.

You have been blocked from further posting in this thread, as this sort of misinformation is helping no one.

 

[L Drago]

"Speed" is a measure that depends upon a choice of coordinates. "Faster speed" has no invariant meaning.

I think that Speed depends relative to something if I am standing and particle accelerator is besides me. With respect to a particle moving in forward direction, I am moving backwards with a very high speed and with respect to a particle moving backwards, I am travelling forward with very high speed.

"Speed" is a measure that depends upon a choice of coordinates. "Faster speed" has no invariant meaning.

If we settle upon inertial coordinates in which the starting and ending events have identical spatial locations in a flat space time then the [suitably integrated] frame-relative speed figures directly into the cumulative elapsed proper times along the two trajectories.$$\Delta t_\text{proper} = \int_\text{start}^\text{end} \frac{dt}{\gamma(v(t))}$$

 

[L Drago]

It may be helpful to note that time dilation is symmetrical, each traveler will observe the other's clock dilated compared to their own proper time. Which seems paradoxical until you take the relativity of simultaneity into account. But time dilation is a comparison of a proper time to a dilated time.

But what has come to be called "differential aging" in this forum is actually a comparison of two proper times. The observers will agree on the difference in proper time.

In the parlance of physics, proper time is a relativistic invariant, meaning all observers will agree on its value. Dilated time is not a relativistic invariant, meaning different observers may disagree on its value.

It means that if a person is travelling in extremely high say 90 percent speed of light in space and I am here on Earth and another person is travelling in 80 percent speed of light. time dilation will occur and we three can disagree on dilated time as it is relative but we have to agree on proper time.

 

[Nugatory]

but we have to agree on proper time.

Proper time between a given pair of events, that is.
And remember that that proper time will correspond to difference between clock readings only for a clock that is at rest using a frame in which both events occur at the point in space.

 

[L Drago]

Proper time between a given pair of events, that is.
And remember that that proper time will correspond to difference between clock readings only for a clock that is at rest using a frame in which both events occur at the point in space.

That means suppose an event A and event B occur in earth. The time period of clock between these two events is called proper time.

 

[robphy]

Proper time between two events depends on the worldline-segment meeting those events.

The interval between two events in Minkowski spacetime is equal to the proper time along the timelike-geodesic segment joining those events (e.g an inertial observer meeting those two events). For the interval, the key word here is “inertial”… “at rest” and “same place” aren’t enough.

 

[jbriggs444]

It means that if a person is travelling in extremely high say 90 percent speed of light in space

As it stands, this is meaningless. One cannot have a speed relative to "space".

and I am here on Earth and another person is travelling in 80 percent speed of light.

Again, 80 percent of the speed of light relative to what?

time dilation will occur

Time dilation is not something that can "occur". It is something that is calculated based on a choice of coordinate system.

and we three can disagree on dilated time as it is relative but we have to agree on proper time.

Yes. Given three frames of reference in relative motion and one trajectory, we can obtain three different numbers for the coordinate time difference (aka "dilated time") between the endpoints. But the proper time elapsed along the trajectory is an invariant quantity upon which all frames must agree.

 

[L Drago]

As it stands, this is meaningless. One cannot have a speed relative to "space".

Again, 80 percent of the speed of light relative to what?

Time dilation is not something that can "occur". It is something that is calculated based on a choice of coordinate system.

Yes. Given three frames of reference in relative motion and one trajectory, we can obtain three different numbers for the coordinate time difference (aka "dilated time") between the endpoints. But the proper time elapsed along the trajectory is an invariant quantity upon which all frames must agree.

Suppose person A is at rest relative to the surface of Earth and Person B is travelling in 80 percent speed of light relative to a planet in solar system say let's take Earth as Person A is also in restaurant relative to its surface and Person C is also travelling in 90 percent speed of light relative to planet Earth
We have to calculate by using SR time dilation.
Dilated time = Actual time / power root of (1-(v²/c²)). These three persons will not agree to dilated time but will agree to proper time. I think this explanation might be correctly worded.

 

[Herman Trivilino]

Dilated time = Actual time / power root of (1-(v²/c²)). These three persons will not agree to dilated time but will agree to proper time. I think this explanation might be correctly worded.

What do you mean by actual time?

You will never understand unless you start thinking about events and the intervals that separate them. It is only in this context that sweeping conclusions like the above make sense.

 

[Ibix]

Suppose person A is at rest relative to the surface of Earth and Person B is travelling in 80 percent speed of light relative to a planet in solar system say let's take Earth as Person A is also in restaurant relative to its surface and Person C is also travelling in 90 percent speed of light relative to planet Earth
We have to calculate by using SR time dilation.
Dilated time = Actual time / power root of (1-(v²/c²)). These three persons will not agree to dilated time but will agree to proper time. I think this explanation might be correctly worded.

Suppose I drew three straight lines on a piece of paper and I told you that line A pointed at the lamp, line B pointed to the TV, and line C pointed at the door. Now I ask you if $a=h\sin\theta$ is the formula to describe those lines' actual length.

That scenario uses Euclidean geometry rather than the Minkowski geometry of spacetime, but otherwise it turns out to be pretty much what you asked. How would you reply? Note that I haven't defined $a$, $h$, $\theta$ or "actual length".

 

[jbriggs444]

Suppose person A is at rest relative to the surface of Earth and Person B is travelling in 80 percent speed of light relative to a planet in solar system say let's take Earth as Person A is also in restaurant relative to its surface and Person C is also travelling in 90 percent speed of light relative to planet Earth

Let me be sure that I have the setup straight.

We have an inertial reference frame. It is the rest frame of the Earth's surface. The problem will be described in terms of this frame.

We have three people: A, B and C. A is at rest in our frame. B is moving inertially at 0.8c in our frame. C is moving inertially at 0.9 c in our frame.

The intent is to treat these three people as three "observers". That is, we will consider each as defining an inertial frame of reference in which he or she is at rest.

We have to calculate by using SR time dilation.

What, exactly, are we calculating?

What is the trajectory for which we will be computing a dilated time?
What is the trajectory for which we will be computing a proper time?

Is there one trajectory? Or three? What are the end points? What is the path between the endpoints?

Dilated time = Actual time / power root of (1-(v²/c²)). These three persons will not agree to dilated time but will agree to proper time.

I agree in principle.

If we had an object traversing an unaccelerated (geodesic) trajectory from a start event to an end event then all three observers could calculate an elapsed coordinate time (aka "dilated time") for the trajectory by dividing the object's elapsed proper time (not "actual time") by $\sqrt{1-v^2/c^2}$. Here, $v$ is, of course, the object's velocity relative to the observer's rest frame.

Alternately, all three observers could calculate the elapsed proper time for the object by multiplying their measured coordinate time difference for the trajectory by $\sqrt{1-v^2/c^2}$.

If the object is traversing an accelerated trajectory then it will not have a single constant velocity $v$. One may have to evaluate an integral.

One can communicate more effectively by using standard terms (e.g. proper time and coordinate time) rather than non-standard terms (e.g. actual time and dilated time).