ask a physicist

[tomBitonti]

Hi,

Yes, I was using demonstration loosely, more meaning by doing some equations on a blackboard.

I follow most of the rest which you have written. What I'm looking for is more about what physical assumptions are allowed at the beginning of the demonstation. Also, what means of measuring time and distance are taken as safe to use. Given the very slight effects at slow speeds, everyday means of measurement don't seem safe to take as reliable, at least not to the level of accuracy which are sufficient to detect the effects.

I ask because of difficulties that I have in recounting the basic demonstration, a difficulty not in doing the math, which is quite simple, but rather in knowing what assumptions are made at the beginning. What is the physical basis for the reasoning which follows?

Thx!

tomB

 

[freyar]

Yes, I was using demonstration loosely, more meaning by doing some equations on a blackboard.

I follow most of the rest which you have written. What I'm looking for is more about what physical assumptions are allowed at the beginning of the demonstation. Also, what means of measuring time and distance are taken as safe to use. Given the very slight effects at slow speeds, everyday means of measurement don't seem safe to take as reliable, at least not to the level of accuracy which are sufficient to detect the effects.

I ask because of difficulties that I have in recounting the basic demonstration, a difficulty not in doing the math, which is quite simple, but rather in knowing what assumptions are made at the beginning. What is the physical basis for the reasoning which follows?

OK, this is a somewhat different question that I thought you were asking before (or what Umbran thought, I guess, but I should say that I like his answer a lot). But the assumptions Einstein made are really just the two that Umbran said: (1) Physics is the same in all inertial reference frames and (2) there is some speed, called c, which is the same in all inertial frames [and also happens to be the speed of light in vacuum]. The math all follows from that. You do seem to be a bit worried about how we think about measurements of distance and time in the actual mathematical derivation --- the answer is that we don't. We're concerned about the underlying physics, not difficulties with measurement, when we're doing a derivation like that. So we imagine that each reference frame has a grid of clocks and rulers spreading throughout all of space. And since we're worried about two different frames moving with respect to each other, the clocks and rulers are ghostly in the sense that they can pass through each other. The point is that we're getting to the idealized measurement, what some perfect measuring device would see. That's why relativity is about the actual properties of space and time, not measurement issues.

 

[Umbran]

What I'm looking for is more about what physical assumptions are allowed at the beginning of the demonstation.

For the gedankenexperiment, clocks are rulers are idealized. The physical assumptions of clocks and rulers don't change the result - they only change whether or not you could detect the result if you actually performed the experiment.

Also, what means of measuring time and distance are taken as safe to use. Given the very slight effects at slow speeds, everyday means of measurement don't seem safe to take as reliable, at least not to the level of accuracy which are sufficient to detect the effects.

When we are discussing the demonstration, for purposes of establishing the logic to create those equations, we don't worry about the details of clocks and rulers. It is an experiment in the imagination, not in the real world.

 

[AbdulAlhazred]

For the gedankenexperiment, clocks are rulers are idealized. The physical assumptions of clocks and rulers don't change the result - they only change whether or not you could detect the result if you actually performed the experiment.



When we are discussing the demonstration, for purposes of establishing the logic to create those equations, we don't worry about the details of clocks and rulers. It is an experiment in the imagination, not in the real world.

Although in all fairness there are pretty accessible modern instruments (modern being meant rather loosely actually) that will do the trick. The interferometer used by Michaelson and Morley in 1887 was quite sensitive for instance, and laser interferometers can quite easily be built today using off-the-shelf components which achieve results good enough to detect differences in the range of something like 1000's of KPH at least. I don't think anyone can detect relativistic effects at the few M/sec^2 typical of everyday human life, but you'd be surprised at how accurate these things can get. I'm not sure you can do a high school physics experiment in a classroom, but you could certainly calculate the relativistic corrections needed for GPS and by how much they change the measured positions, with a few simplifications.

 

[Umbran]

Although in all fairness there are pretty accessible modern instruments (modern being meant rather loosely actually) that will do the trick. The interferometer used by Michaelson and Morley in 1887 was quite sensitive for instance, and laser interferometers can quite easily be built today using off-the-shelf components which achieve results good enough to detect differences in the range of something like 1000's of KPH at least. I don't think anyone can detect relativistic effects at the few M/sec^2 typical of everyday human life, but you'd be surprised at how accurate these things can get. I'm not sure you can do a high school physics experiment in a classroom, but you could certainly calculate the relativistic corrections needed for GPS and by how much they change the measured positions, with a few simplifications.

Yes, humans are capable of measuring the impacts.

But the point is that the example stated is a gedankenexperiment - a *thought* experiment, to make the logic plain. And, for that, we don't have to worry about the quality of the measuring implements, because they don't exist! Einstein didn't run the experiment with some set of real-world instruments! We can, in thought, crank up the speeds as high as we want, so the effects are large, and we can imagine them observed with simple wind-up clocks, if we want. This is the power of thought.

 

[tomBitonti]

For the gedankenexperiment, clocks are rulers are idealized. The physical assumptions of clocks and rulers don't change the result - they only change whether or not you could detect the result if you actually performed the experiment.

When we are discussing the demonstration, for purposes of establishing the logic to create those equations, we don't worry about the details of clocks and rulers. It is an experiment in the imagination, not in the real world.

This statement encompasses a lot!

2) The laws of physics are the same in all inertial frames of reference

That is, it pulls a notion that an initial frame of reference is a distinguished frame, and that physical properties such as the rate of passage of time (as measured by common physical processes, say, decay rates) will be measured as the same thing for different observers in the same initial frame, and similarly, that distances can be reliably measured (say, as a count of wavelengths of light as emitted, again, by common physical processes), and will yield a consistent result by different observers, and that these measurements will be stable over time.

Then, the notion of an idealized clock must be presented as physically meaningful, even if no actual ideal clock can be made. And, it turns out that certain physical processes can be used to make very accurate clocks. As well, one must demonstrate that if a number of idealized clocks may be created, they will be shown to record the passage of time uniformly, so that any irregularities must be shared by the clocks and by the observer. It must also be shown that an idealized clock can be transported to various locations and remain accurate. (Knowing the results of the experiment, we will know that the clocks will show slightly different times after they are transported, but, they will still show the same rate of passage.)

This would all seem to be overly pedantic, except that the experiment will go on to show that observers in different frames of reference will not obtain the same results, so these sorts of considerations are not outside of the realm of the experiment which is being done.

Thx!
TomB

 

[AbdulAlhazred]

Yes, humans are capable of measuring the impacts.

But the point is that the example stated is a gedankenexperiment - a *thought* experiment, to make the logic plain. And, for that, we don't have to worry about the quality of the measuring implements, because they don't exist! Einstein didn't run the experiment with some set of real-world instruments! We can, in thought, crank up the speeds as high as we want, so the effects are large, and we can imagine them observed with simple wind-up clocks, if we want. This is the power of thought.

Sure, I just get the impression that tomBitonti was looking for some sort of "hey, you can actually play with this instrument and SEE some sort of relativistic effect".

There ARE actually relativistic effects that are apparent in everyday life, they're just so common that we don't really recognize them as such. The color of gold for instance is the result of relativistic effects within the large electron shell structure of gold atoms. Its just not something we normally think about in those terms.

 

[tomBitonti]

Sure, I just get the impression that tomBitonti was looking for some sort of "hey, you can actually play with this instrument and SEE some sort of relativistic effect".

There ARE actually relativistic effects that are apparent in everyday life, they're just so common that we don't really recognize them as such. The color of gold for instance is the result of relativistic effects within the large electron shell structure of gold atoms. Its just not something we normally think about in those terms.

That would be nice, but, that's not quite what I'm looking for.

What I'm looking for is more along of these lines:

The thought experiment envisions an ideal clock. How do we know that such a notion is even for an idealized device at all reasonable? If transporting a clock affects what time it measures, even returning to the starting point, what assurance do I have that transporting a clock to a distant point and using it to measure time there for an observer here is valid?

Similarly, built into the experiment is a statement that, in a rest frame, different observers in that frame can reliably measure distances.

The point is that the experiment relaxes one common assumption -- that durations and distances are the same for all observers -- but allows to stand other common assumptions. If one takes that notion from the experiment, of relaxing a usual assumption, but doesn't have guidance on what should be assumed and what should not be assumed, working through the thought experiment gets to be difficult.

Thx!
TomB

 

[AbdulAlhazred]

That would be nice, but, that's not quite what I'm looking for.

What I'm looking for is more along of these lines:

The thought experiment envisions an ideal clock. How do we know that such a notion is even for an idealized device at all reasonable? If transporting a clock affects what time it measures, even returning to the starting point, what assurance do I have that transporting a clock to a distant point and using it to measure time there for an observer here is valid?

Similarly, built into the experiment is a statement that, in a rest frame, different observers in that frame can reliably measure distances.

The point is that the experiment relaxes one common assumption -- that durations and distances are the same for all observers -- but allows to stand other common assumptions. If one takes that notion from the experiment, of relaxing a usual assumption, but doesn't have guidance on what should be assumed and what should not be assumed, working through the thought experiment gets to be difficult.

Thx!
TomB

What do you mean by 'reasonable'. We can imagine a gridwork of clocks associated with each point in space-time where they all start out with their 'hands' measuring exactly the same and then move forward in time and see what they look like as we do so. In REALITY we'd have to pick some points, figure out what to set each clock to based on our theory of relativity such that we'd SEE the same hand positions on each once they got to their assigned locations and velocities. There simply is no other way to define 'what time do I think it is over there' except 'what am I seeing on the face of a clock which I perceive to be at that location now'. Note how different this is from classical mechanics where one could at least posit infinite velocities and some sort of notion of 'absolute time' existed.

This is why it is said that Relativity stems from 'Machian' principles, there simply are no absolutes, except one, that every observer will see a consistent time line under which the same laws of physics will apply, even if no 2 of them can agree on what specific events happened in what order or which one caused the other.

 

[Umbran]

The thought experiment envisions an ideal clock. How do we know that such a notion is even for an idealized device at all reasonable?

Oh, that's easy - because we don't actually care about the clock.

You see, clocks are made by people. They don't exist naturally. Therefore, the nature of the universe *must be independent of clocks*! Time and distance exist whether or not we have instruments to measure them!

If transporting a clock affects what time it measures, even returning to the starting point, what assurance do I have that transporting a clock to a distant point and using it to measure time there for an observer here is valid?

Well, that is one of the base assumptions - that the basic laws of physics are the same in all inertial frames of reference. If you want to consider that it is incorrect - have at you. Find the place it isn't true, and maybe the Nobel Committee will give you an award.

However... go out on a clear night (hopefully away from a city) and look up. What do you see? Stars.

If we accept that the laws of time and space vary from place to place, we accept the likely need to come up with a unique explanation for each and every star. When we see so many very similar phenomenon, everywhere we look, it rather strains credulity that the laws aren't the same all over the place. Moreover, we can see very well that the laws of the universe hold pretty uniformly over this rock that we shall, for convenience, call "Earth", and, in fact, over the space of the solar system - we have sent out devices with measuring equipment, and they continue to operate as expected, without huge anomalies that can't be explained.

So - the laws are all the same in our neighborhood. And in our galaxy. If there's some place in our sight that's substantially different, we should be able to see the difference when we look out into space. But we don't. So, the observable universe seems to have the same laws.

That's not enough for you? Wow. Tough crowd.