Is Time Slowing or Are Processes Slowing Near High Gravity and Speeds?

[1977ub]

Use a set of inertial rods and clocks where the clocks are synchronized using Einsteins convention. It can certainly be done if you are accelerating. You will not be at rest (other than momentarily) in such a frame, but there is no reason that you must use a coordinate system where you are at rest.

I think over here I was discouraged from doing something like this. Einstein method doesn't agree with Rindler method, etc. Apples & oranges?

https://www.physicsforums.com/showthread.php?t=668580&highlight=pallen&page=6

 

[Nugatory]

I think over here I was discouraged from doing something like this. Einstein method doesn't agree with Rindler method, etc. Apples & oranges?

https://www.physicsforums.com/showthread.php?t=668580&highlight=pallen&page=6

DaleSpam is telling to you use an inertial frame in which you are accelerating; in that other thread you were being warned away from using a non-inertial frame in which you were at rest.

Confusions of this sort are the reason why I try very hard to avoid speaking of "the reference frame of <somethng>" or "the observer's reference frame" and the like

 

[1977ub]

DaleSpam is telling to you use an inertial frame in which you are accelerating; in that other thread you were being warned away from using a non-inertial frame in which you were at rest.

If I am accelerating, and if I will not be able to determine in a straightforward way which particular times and distances particular events have happened, not able to use any methods which operate in an IRF, how will I then be able to construct the Minkowski metric which describes the view from *any* IRF? It's all well and good for us *outside* of the situation, analyzing the motion from the perspective of a perfectly flat spacetime, and at rest.

 

[Fredrik]

If I am accelerating, and if I will not be able to determine in a straightforward way which particular times and distances particular events have happened, not able to use any methods which operate in an IRF, how will I then be able to construct the Minkowski metric which describes the view from *any* IRF? It's all well and good for us *outside* of the situation, analyzing the motion from the perspective of a perfectly flat spacetime, and at rest.

The question is a bit odd, since the metric is a property of spacetime, not a property of your world line. I'm guessing that what you have in mind is to apply the standard synchronization convention to a non-geodesic world line. The result will be a coordinate system that can't be defined on all of spacetime. It's a local coordinate system, not a global one. Nothing wrong with that though.

The suggestion that you've been given is to use the fact that the tangent your world line at any point on it is a geodesic, which can be taken to be the t axis of an inertial coordinate system. This coordinate system is certainly easier to work with.

 

[1977ub]

The question is a bit odd, since the metric is a property of spacetime, not a property of your world line. I'm guessing that what you have in mind is to apply the standard synchronization convention to a non-geodesic world line. The result will be a coordinate system that can't be defined on all of spacetime. It's a local coordinate system, not a global one. Nothing wrong with that though.

The suggestion that you've been given is to use the fact that the tangent your world line at any point on it is a geodesic, which can be taken to be the t axis of an inertial coordinate system. This coordinate system is certainly easier to work with.

Again, all of this seems to assume that I am floating above all of this information and know information about my world line, how to describe a tangent to it, etc. I asked about how to do this in the context of the conversation that was going on. Can you describe how to experimentally derive or construct the "minkowski space" from the POV of an accelerating observer making empirical observations?

 

[Dale]

I think over here I was discouraged from doing something like this. Einstein method doesn't agree with Rindler method, etc.

You asked how to experimentally construct a Minkowski metric, I answered. How you are accelerating is irrelevant, as is the Rindler method.

 

[Dale]

If I am accelerating, and if I will not be able to determine in a straightforward way which particular times and distances particular events have happened, not able to use any methods which operate in an IRF

I told you a straightforward way to use methods which operate in an IRF.

 

[Dale]

Can you describe how to experimentally derive or construct the "minkowski space" from the POV of an accelerating observer making empirical observations?

There are a number of ways. I already gave the most basic way. You can also use an accelerometer and radar. You can also use a GPS-like system. I am sure there are other ways.

 

[1977ub]

Use a set of inertial rods and clocks where the clocks are synchronized using Einsteins convention. It can certainly be done if you are accelerating. You will not be at rest (other than momentarily) in such a frame, but there is no reason that you must use a coordinate system where you are at rest.

I told you a straightforward way to use methods which operate in an IRF.

I am accelerating. How do I access "inertial" rods and clocks?

 

[1977ub]

Anyhow I barely recall the point I was trying to make. Thanks, everyone.

 

[pervect]

If I am accelerating, and if I will not be able to determine in a straightforward way which particular times and distances particular events have happened, not able to use any methods which operate in an IRF, how will I then be able to construct the Minkowski metric which describes the view from *any* IRF? It's all well and good for us *outside* of the situation, analyzing the motion from the perspective of a perfectly flat spacetime, and at rest.

The Lorentz interval between all pairs of "nearby" points determines the geometry.

There isn't any argument about how to choose a nearly inertial (and usually, co-moving) frame for _nearby_ events (which I'll call points from now on), which one can use to measure said interval. If the points are too far away from each other, you do start to see errors or ambiguities (depending on your interpretation) due to curvature. The solution to this dilemma is to choose points that are closer together, so these errors/ambiguities do not arise.

When you pick a coordinate system, then, you can choose some point with some coordinates (p,q,r,s), and some nearby point where one or more of the coordinates varies. You then determine the metric coefficients by fitting the measured Lorentz intervals to the ones you compute from the quadratic form of the metric.

This gives you the values of the metric coefficeints at the point (p,q,r,s). You repeat as desired at another point.

Sort of an aside, but while there are many methods to determine "distance in the large", one of the most intuitive is using Fermi Normal coordinates. But I suppose that would be material for another post, to treat it properly.

 

[Dale]

I am accelerating. How do I access "inertial" rods and clocks?

Take some rods and clocks and let go of them.

 

[Alain2.7183]

Can you describe how to experimentally derive or construct the "minkowski space" from the POV of an accelerating observer making empirical observations?

I like this description:

https://sites.google.com/site/cadoequation/cado-reference-frame

 

[1977ub]

I like this description:

https://sites.google.com/site/cadoequation/cado-reference-frame

Not done yet... seems like you need to have access to your v as measured by observer at the resting origin?

 

[1977ub]

Take some rods and clocks and let go of them.

Sounds like they're overboard then and I no longer know with certainty how far away they are...

 

[Fredrik]

Again, all of this seems to assume that I am floating above all of this information and know information about my world line, how to describe a tangent to it, etc.

Yes, that's right.

I asked about how to do this in the context of the conversation that was going on. Can you describe how to experimentally derive or construct the "minkowski space" from the POV of an accelerating observer making empirical observations?

I don't know what that means. Do you want to prove by experiment that spacetime is Minkowski spacetime? Then you got it backwards. That's not how physics works. You define the theory, and use it to make predictions about results of experiments. Then you do experiments to find out how accurate those predictions are. If the predictions are good, we say that the theory is good. (I probably just don't understand what it is you want to do).

 

[Dale]

Sounds like they're overboard then and I no longer know with certainty how far away they are...

As long as they cover the region of spacetime you are interested in then you have a Minkowski metric there. Whether or not that region covers you is not important, but if it does cover you then you do know the distance.

 

[Nugatory]

If I am accelerating, and if I will not be able to determine in a straightforward way which particular times and distances particular events have happened, not able to use any methods which operate in an IRF, how will I then be able to construct the Minkowski metric which describes the view from *any* IRF? It's all well and good for us *outside* of the situation, analyzing the motion from the perspective of a perfectly flat spacetime, and at rest.

This is easy in a thought experiment... And important, because I'm not sure you have fully understood what it means to say that a frame of reference is nothing more than a way of assigning coordinates to events:

Before you turn on your rocket engines or whatever to start accelerating, construct a three-dimensional rigid lattice of one-meter rods that fills the entire space that you'll be flying through. At each intersection of the rods, place an observer equipped with a synchronized clock, a pad of paper, and a pencil; these observers are of course all at rest relative to one another and not accelerating. Whenever any observer sees something interesting happen right exactly where he is, he writes down what happened and when according to his clock it happened.

Now you can go ahead and do your accelerating, or conduct any other experiment you please, involving any number of spaceships flying in whatever directions at whatever speeds are interesting.

At some later time, we will go back and at our leisure collect each observers' paper record of what happened at various times at his point in space and correlate them to form a complete description of what happened when and who moved where how fast according to this particular lattice of observers.

The collection of paper records is an inertial frame of reference.
1) Anyone can set up a lattice of rods, synchronized clocks, and observers moving at any speed they please; the only thing that we require is that they all be at rest relative to one another and not accelerating.
2) There is nothing special to me about the lattice of rods, synchronized clocks, and observers that happens to be at rest relative to me. I can use their paper records to figure out what was happening in the region of space covered by the lattice, but I could just as easily choose to collect the paper records from some other lattice of rods, synchronized clocks, and observers.
3) It is not possible (and this is the point of the thread you referenced in #106) to construct a such a lattice of rods, synchronized clocks, and observers that is accelerating.
4) Even if you are accelerating, at any given moment you are traveling at some speed, and we can construct a lattice of rods, synchronized clocks, and observers all at rest relative to you at that moment. This is a "momentarily comoving inertial frame" or MCIF, and the first step in understanding any scenario involving acceleration and special relativity is to find an MCIF.

 

[1977ub]

Yes. of course. I was referring only to the simple case of a perpetually accelerating observer. He has all by himself no IRF. I was only attempting to refer to the "how does Minkowski metric cause artifacts" question response to my comment about IRF practice/policy/habit giving rise to twin paradox etc.

4) Even if you are accelerating, at any given moment you are traveling at some speed, and we can construct a lattice of rods, synchronized clocks, and observers all at rest relative to you at that moment. This is a "momentarily comoving inertial frame" or MCIF, and the first step in understanding any scenario involving acceleration and special relativity is to find an MCIF.

Even if "you" are accelerating... "we" can construct... this is my point. In the abstract, after the fact, "we" can do this with our coordinated measurements, but for "you" who are accelerating, this is not possible. It takes one or more inertial observers to create this. I was really only attempting to make such a minor point, and it gave rise to all this.

 

[Nugatory]

I am accelerating. How do I access "inertial" rods and clocks?

You don't need to access them. All you need to do is to calculate how they would behave if you could access them.

No matter what you're doing, no matter how you're moving, whether you're accelerating or not, you can choose any coordinate system (aka frame of reference, aka rule for assigning coordinates to events) that you please. There is nothing at all special about the non-inertial frame in which accelerating you is at rest, even for you.

(You might reasonably demand experimental evidence that these calculations accurately describe what you would see if you could access the inertial rods and clocks... And you can, in principle, do that through the procedure that I describe in #123.)

 

[ghwellsjr]

Even if "you" are accelerating... "we" can construct... this is my point. In the abstract, after the fact, "we" can do this with our coordinated measurements, but for "you" who are accelerating, this is not possible. It takes one or more inertial observers to create this. I was really only attempting to make such a minor point, and it gave rise to all this.

Do you know how to do this for an inertial observer?

Is it only because an observer is accelerating that you think that it can no longer be done?

 

[dayalanand roy]

Dear D English
Welcome to this thread. Thanks.

 

[1977ub]

You don't need to access them. All you need to do is to calculate how they would behave if you could access them.

Indeed. I think this is precisely what I was told I would be unable to do *unamiguously* in the earlier thread. I am accelerating. I see a light pulse from the 'origin'. I don't know when it was sent because I can't tell how far it traveled. I suppose if I can live with the ambiguity I can select one method.

While AO would have no difficulty making some choices to set up some coordinate system, the ambiguity means you can't give a single preferred answer to RF origin's clock speed - it depends on which choices you make for setting up the coordinate system.

 

[Dale]

Indeed. I think this is precisely what I was told I would be unable to do *unamiguously* in the earlier thread.

No, that is a completely different topic. The ambiguity described there was an ambiguity in terminology, not physics. The phrase "X's frame" has no standardized definition if X is non-inertial. But that is just a matter of terminology and if an authoritative source were to standardize the meaning then the ambiguity would be resolved.

That terminology ambiguity in no way implies an ambiguity in the physics of non inertial observers or frames.

 

[1977ub]

That terminology ambiguity in no way implies an ambiguity in the physics of non inertial observers or frames.

I was interested in the physics FOR / FROM "you" as a non-inertial observer. Not the physics of "we" non-inertial observers measuring an accelerating observer or object.

 

[Dale]

I was interested in the physics FOR / FROM "you" as a non-inertial observer. Not the physics of "we" non-inertial observers measuring an accelerating observer or object.

Again, there is no ambiguity in the physics, only the terminology.

 

[big_bounce]

I know it's late in the discussion, but I have a question relate to the topic .

I realized that length contraction and time dilation are two sides of the same coin .

Respect to this :

If i will make a freezer near absolute zero ( Or even exactly absolute zero ) in Earth and i will come into it and after 50 years ( respect to Earth's calendar ) i come out from it .
Will i find myself younger than you ?

If temperature gets lower and lower , Does rate of change time get slower and slower ?

 

[Dale]

The second is already defined wrt absolute 0.

http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html

 

[Fredrik]

You can slow down the rate of chemical reactions by lowering the temperature. But you can't slow down all clocks this way, so it wouldn't make sense to say that time has been slowed down.

 

[ghwellsjr]

Absolute zero for the caesium atom simply means it is at rest.

This quote from the above link is redundant:

This definition refers to a caesium atom at rest at a temperature of 0 K.

If it is at rest, its temperature is 0 K.

 

[Fredrik]

Absolute zero for the caesium atom simply means it is at rest.

This quote from the above link is redundant:



If it is at rest, its temperature is 0 K.

That page included a comment about the statement you dismissed.

This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K.​

So it appears that they were talking about its environment.

 

[ghwellsjr]

That page included a comment about the statement you dismissed.

This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K.​

So it appears that they were talking about its environment.

The environment they are talking about is other nearby caesium atoms. The chamber containing these atoms will not be anywhere near 0 K. The whole idea here is that caesium atoms that are not at rest, by definition, move away from the caesium cloud at 0 K and the goal is to keep them away or to stop them as they join the cloud.

The paper is not concerned with how in practice an atomic clock can be built, only that if the atoms are not at 0 K, then an adjustment must be made in the timing of the clock.

 

[dayalanand roy]

Dear all learned participants to this thread

I wish to express my deepest regards to all of you as you all have enabled me to learn a lot.
Dayalanand