High School Time dilation, relativistic mass and fuel consumption

[PeterDonis]

What I'm saying is that rest energy and mass are the same thing expressed in different units

If we interpret "mass" in the usual modern sense of "invariant mass", yes. (What's more, if we use "natural" units in which $c = 1$, they aren't even in different units.)

that it's redundant and potentially confusing to keep them both around once this has been established

Agreed.

and that "rest energy" is the better choice

I disagree. Your argument is basically that since we say "total energy" instead of "relativistic mass", we should say "rest energy" instead of "rest mass". But that argument assumes that "total energy" and "rest energy" are the same kind of thing, physically. They're not. Rest mass is an invariant; total energy is not.

Also, FWIW, physicists in general appear to use "rest mass" when talking about invariant mass. Using "rest energy" is extremely rare in the modern literature. So whatever your or my opinion might be, the physics community in general has settled on "rest mass" (or "invariant mass") being the standard usage.

 

[SiennaTheGr8]

Also, FWIW, physicists in general appear to use "rest mass" when talking about invariant mass. Using "rest energy" is extremely rare in the modern literature. So whatever your or my opinion might be, the physics community in general has settled on "rest mass" (or "invariant mass") being the standard usage.

Yes, and that's my point: I think it's a bad convention.

I disagree. Your argument is basically that since we say "total energy" instead of "relativistic mass", we should say "rest energy" instead of "rest mass".

That's part of my argument. There's also the question of dimensions/units (if not using $c = 1$) and the question of symbols (something $E$-ish like $\mathcal{E}$ or $E_0$ vs. $m$).

But that argument assumes that "total energy" and "rest energy" are the same kind of thing, physically. They're not. Rest mass is an invariant; total energy is not.

I don't think whether they're "the same kind of thing, physically" is such a straightforward question. Yes, one is the Lorentz-invariant norm of the four-vector that the other is the frame-dependent time-component of, but one is also the other when reckoned in the rest frame.

You could make the same argument about "coordinate time" and "proper time." And if we called "proper time" some other term that didn't have "time" in it and gave it a different unit and a symbol that wasn't $t$-ish, I'd likewise say that this isn't as learner-friendly as it could be.

Cheers, Peter.

 

[PeterDonis]

I don't think whether they're "the same kind of thing, physically" is such a straightforward question.

It is. They're not.

one is also the other when reckoned in the rest frame

Yes, in one particular frame. Which just highlights that total energy is frame-dependent and invariant mass is not.

You could make the same argument about "coordinate time" and "proper time."

Indeed you could. And to me, that's an argument for figuring out something besides "time" to attach the "coordinate" label to. Unfortunately physics terminology is not always logical.

if we called "proper time" some other term that didn't have "time" in it

No, if we called coordinate time some other term that didn't have "time" in it, to emphasize the fact that "time", the thing we actually experience and measure, the physical thing, is proper time.

I think doing that would be more learner friendly than what we do now. As evidence I give you the thousands of PF threads, including this one, that involve the mistaken belief that coordinate time is somehow physically meaningful, because it's called "time".

 

[PainterGuy]

Thank you, everyone, for your time.

There are no Newtonians left. There isn't a debate. If you want to push the theory that Newtonian physics should be restored, you are in the wrong place.

I did not say any such thing. I'm only trying to learn and each of us learn differently and each of us have different level of intelligence and ability to express themselves. I'm trying to learn the basic concepts in layman terms or you can say in 'pop science' fashion. I hope you don't mind it. Thanks!

So it is slurping up air from the vacuum, burning gasoline from the fuel tank, and rotating tires to produce friction against a non-existent roadbed. We are to evaluate this for efficiency.

An evaluation of efficiency calls for a detailed understanding of the mechanism. None has been forthcoming.

My apologies, Sir, that I couldn't frame the question properly but I made an honest attempt. But I hope now you understand what I was trying to say and the point I was trying to make.

Now we can calculate the fuel consumption rate: It's gamma squared times larger than what they had calculated.

So, finally, it's concluded that Newtonians would be see that more fuel has been consumed than was originally calculated. The mass increase during the trip was real. In their attempt to understand this difference, they will try to find an explanation. I wanted to clarify three more related points.

Question 1:
There is still one point which bothers me. During the trip, the pilot cannot know if local time has been dilated compared to that of the Earth and also he cannot find that mass of rocket has increased but he can definitely see the gauge and see that more fuel is being consumed than was calculated. Would the pilot be able to notice the difference?

Question 2:
Let's assume that there was a clock present on the rocket which wasn't used at all during the trip. Newtonians notice that the time on this clock lags behind the ones on earth. They carefully examine the engine and mass of the rocket and find no problem with it. In short, something has happened to the time and it's permanent but whatever happened to either rocket mass/engine was only true for the duration of trip.

Anyway, I stumbled upon the following text and this relates to what I'm saying above and what is confusing me, https://arxiv.org/ftp/arxiv/papers/0707/0707.2426.pdf, and the first para under 'Introduction' interested me.

"In this discussion, the speed of light c is assumed to be invariant. The physical reality is only time dilation
by velocity. The constancy of the speed of light causes the time dilation by motion. Mass m and length x are
also invariant though mass and length appear to be variant through the Lorentz transformation of reference
time. That is, Lorentz contraction of length and inertial mass increase can also be explained by the Lorentz
transformation of reference time".

In my view, if local time has been dilated then it would result into length contraction as well. In other words, length contraction results from the time dilation. For example, to an observer on the Earth, the muon travels at 0.950 c for 7.05 μs from the time it is produced until it decays. Thus it travels a distance L0 = vΔt = (0.950)(3.00 × 108 m/s)(7.05 × 10−6 s) = 2.01 km relative to the Earth. In the muon’s frame of reference, its lifetime is only 2.20 μs. It has enough time to travel only L0 = vΔt0 = (0.950)(3.00 × 108 m/s)(2.20 × 10−6 s) = 0.627 km. The distance between the same two events (production and decay of a muon) depends on who measures it and how they are moving relative to it. Source: https://courses.lumenlearning.com/physics/chapter/28-3-length-contraction/

I think it'd be appropriate to quote a passage from Wikipedia. I'm sorry that some of the math isn't appearing properly but you can see the original reference.

"Concepts that were similar to what nowadays is called "relativistic mass", were already developed before the advent of special relativity. For example, it was recognized by J. J. Thomson in 1881 that a charged body is harder to set in motion than an uncharged body, which was worked out in more detail by Oliver Heaviside (1889) and George Frederick Charles Searle (1897). So the electrostatic energy behaves as having some sort of electromagnetic mass {\displaystyle m_{em}=(4/3)E_{em}/c^{2}}

, which can increase the normal mechanical mass of the bodies.[9] [10]

Then, it was pointed out by Thomson and Searle that this electromagnetic mass also increases with velocity. This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory. He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass {\displaystyle m_{L}=\gamma ^{3}m}

parallel to the direction of motion and the mass {\displaystyle m_{T}=\gamma m}

perpendicular to the direction of motion (where {\displaystyle \gamma =1/{\sqrt {1-v^{2}/c^{2}}}}

is the Lorentz factor, v is the relative velocity between the aether and the object, and c is the speed of light). Only when the force is perpendicular to the velocity, Lorentz's mass is equal to what is now called "relativistic mass". Max Abraham (1902) called {\displaystyle m_{L}}

longitudinal mass and {\displaystyle m_{T}}

transverse mass (although Abraham used more complicated expressions than Lorentz's relativistic ones). So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity.[11] [12] [13]"
Source: https://en.wikipedia.org/wiki/Mass_in_special_relativity#Transverse_and_longitudinal_mass

Question 3:
To me, two different concepts are being mixed up by the term 'length contraction' here. When mass is moving really fast, it gets deformed and it results into the length contraction of mass. But at the same time when a mass is moving really fast, the distance traveled by it also gets shortened due to the time dilation so this is another type of length contraction involving 'distance traveled'.

"Length contraction was postulated by George FitzGerald (1889) and Hendrik Antoon Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment and to rescue the hypothesis of the stationary aether (Lorentz–FitzGerald contraction hypothesis).[2][3] Although both FitzGerald and Lorentz alluded to the fact that electrostatic fields in motion were deformed ("Heaviside-Ellipsoid" after Oliver Heaviside, who derived this deformation from electromagnetic theory in 1888), it was considered an ad hoc hypothesis, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones. In 1897 Joseph Larmor developed a model in which all forces are considered to be of electromagnetic origin, and length contraction appeared to be a direct consequence of this model."
Source: https://en.wikipedia.org/wiki/Length_contraction#History

I think what you're asking about can be answered by looking at the way particle accelerators work. It takes a lot more energy to accelerate the particles than what is predicted using Newtonian physics.

Yes, you have it right.

Thank you!

 

[PeroK]

Anyway, I stumbled upon the following text and this relates to what I'm saying above and what is confusing me, https://arxiv.org/ftp/arxiv/papers/0707/0707.2426.pdf, and the first para under 'Introduction' interested me.

1) The paper you link to is essentially nonsense. You are never going to learn SR by reading papers like the one above.

2) You still have fundamental misconceptions about SR. We can't really help you unless you willing to try to learn SR properly. For example:

In my view, if local time has been dilated then it would result into length contraction as well. In other words, length contraction results from the time dilation ...

This reveals a fundamental misunderstanding of SR.

The first chapter of Morin's undergraduate text on SR is available free online. I suggest you study it:

http://www.people.fas.harvard.edu/~djmorin/Relativity Chap 1.pdf

My advice is to start afresh with Morin. Try to put everything you think you know about SR to one side and try to learn it properly.

At the moment you are simply floundering in a sea of misconceptions.

 

[Ibix]

So, finally, it's concluded that Newtonians would be see that more fuel has been consumed than was originally calculated. The mass increase during the trip was real.

Not really. They're just using an incorrect formula for the relationship between force, mass and acceleration. It's a good approximation at low speeds, but even then it's an approximation - just one that they failed to notice.

During the trip, the pilot cannot know if local time has been dilated compared to that of the Earth and also he cannot find that mass of rocket has increased but he can definitely see the gauge and see that more fuel is being consumed than was calculated. Would the pilot be able to notice the difference?

Local time has not been dilated. I don't think that sentence means anything, to be honest. The pilot will observe that each free-floating clock is ticking slowly, but they have been mis-set so that each one is a little ahead of its predecessor giving the appearance that they, collectively, tick fast (if he hadn't noticed that each one was ticking slowly).

The mass of the rocket hasn't increased - you're just using a wrong relationship between mass and acceleration.

There will be many things that the pilot could notice. Obviously, that he has to monkey around with his acceleration in order to maintain profile. That the Doppler shift of signals from Earth does not match non-relativistic predictions. The clocks, as noted above (you can't deny the pilot his heart rate as a crude onboard clock). The distance markers will not pass at the expected rate.

To me, two different concepts are being mixed up by the term 'length contraction' here. When mass is moving really fast, it gets deformed and it results into the length contraction of mass. But at the same time when a mass is moving really fast, the distance traveled by it also gets shortened due to the time dilation so this is another type of length contraction involving 'distance traveled'.

Yes, this is extremely confused. Length contraction has nothing to do with mass. First, just forget relativistic mass. It's nothing but a distraction - in terms of pedagogy, I think it's best described as an attempt to pretend that relativity isn't more complicated than Newtonian physics. Which is blatantly untrue and comes back to bite, hard, later on.

Furthermore, length contraction and time dilation don't cause one another. Nor does the constancy of the speed of light cause time dilation. I strongly suspect that your problem here is that you are attempting to reason about relativity based on time dilation and length contraction, which are special cases of the Lorentz transforms, in circumstances where they do not apply. I think this because length contraction is not two phenomena, and you have not mentioned the Lorentz transforms at all.

 

[Ibix]

At the moment you are simply floundering in a sea of misconceptions.

My reading of this too.

 

[Nugatory]

Question 1:
There is still one point which bothers me. During the trip, the pilot cannot know if local time has been dilated compared to that of the Earth and also he cannot find that mass of rocket has increased but he can definitely see the gauge and see that more fuel is being consumed than was calculated. Would the pilot be able to notice the difference?

What he is calculating is the amount of fuel required to maintain his proper acceleration between his departure and his arrival at his destination. This calculation is completely unrelated to any observations or measurements made by anyone not on the ship; his undilated clock measuring his proper time is all he needs,

He can do the calculation incorrectly by assuming Newtonian physics, or he can do it correctly using relativistic physics. The fuel gauge will of course show the correct answer for fuel consumed, so if it is sensitive enough to he will notice.

Anyway, I stumbled upon the following text and this relates to what I'm saying above and what is confusing me, https://arxiv.org/ftp/arxiv/papers/0707/0707.2426.pdf

It’s garbage, and stuff like this is why this forum has its rule about acceptable sources. You will be better served by spending some quality time with a real textbook; I’m partial to Taylor and Wheeler’s “Spacetime Physics” but there are many good choices.

Question 2:
Let's assume that there was a clock present on the rocket which wasn't used at all during the trip. Newtonians notice that the time on this clock lags behind the ones on earth. They carefully examine the engine and mass of the rocket and find no problem with it. In short, something has happened to the time and it's permanent but whatever happened to either rocket mass/engine was only true for the duration of trip.

Careful... how do we compare the two clocks to come to this conclusion? The rocket clock is measuring a path through spacetime starting at the event “on Earth ready for departure” and ending at the event “arrived at destination”; the Earth clock is a measuring a different path through spacetime starting at the same event but ending at the completely different event “earth observer checks their clock to see what it reads at the same time as the ‘arrived at destination’ event”. This comparison doesn’t tell us anything about the clocks, which are both ticking at a rate of one second per second because that’s what well-designed clocks do. It just tells us that different paths through spacetime have different lengths, a result that is analogous to the way that automobile odometers tick off different numbers of kilometers on different paths through space.

An important point here is how we chose the endpoint event for the earthbound clock’s path through spacetime. We said the path we’re measuring ends “at the same time” on Earth as the arrival event at the distant planet - but because of the relativity of simultaneity (if you are not familiar with that concept, google for “Einstein train simultaneity and read some of our many threads on the subject) that’s a somewhat arbitrary choice. The discrepancy in clock readings has nothing to do with “something has happened to time” and everything to do with us measuring g two different things with no particular reason to think they are related.

 

[SiennaTheGr8]

But that argument assumes that "total energy" and "rest energy" are the same kind of thing, physically. They're not. Rest mass is an invariant; total energy is not.

I don't think whether they're "the same kind of thing, physically" is such a straightforward question.

It is. They're not.

...if you've defined "kind of thing, physically" as whether or not a thing is invariant.

Yes, one is the Lorentz-invariant norm of the four-vector that the other is the frame-dependent time-component of, but one is also the other when reckoned in the rest frame.

Yes, in one particular frame. Which just highlights that total energy is frame-dependent and invariant mass is not.

No, it highlights that there's obviously a sense in which "rest energy" and "total energy" can be regarded as the "same kind of thing, physically": in any inertial frame, $E = E_0 + E_k = \gamma E_0$.

You could make the same argument about "coordinate time" and "proper time."

Indeed you could. And to me, that's an argument for figuring out something besides "time" to attach the "coordinate" label to. Unfortunately physics terminology is not always logical.

And if we called "proper time" some other term that didn't have "time" in it and gave it a different unit and a symbol that wasn't $t$-ish, I'd likewise say that this isn't as learner-friendly as it could be.

No, if we called coordinate time some other term that didn't have "time" in it, to emphasize the fact that "time", the thing we actually experience and measure, the physical thing, is proper time.

I think doing that would be more learner friendly than what we do now. As evidence I give you the thousands of PF threads, including this one, that involve the mistaken belief that coordinate time is somehow physically meaningful, because it's called "time".

!

I instinctively disagree—strongly—that this would help beginners, but it's a bold and thought-provoking perspective.

 

[vanhees71]

In my experience the approach to teach SRT from the very beginning in terms of Minkowski space and using invariant Minkowski-space quantitities (i.e., tensors, including scalars and vectors) avoids a lot of confusion particularly for beginners. It's one of the great features in the natural sciences that you don't need to learn old-fashioned notions but use the most convenient and established modern ones, and the 4D formalism is much more clear than some old-fashioned notation from the past. This holds the more true, because if you want to go on further and learn GR you cannot even formulate it without sticking to the tensor formulation.

 

[Janus]

Thank you, everyone, for your time.
I did not say any such thing. I'm only trying to learn and each of us learn differently and each of us have different level of intelligence and ability to express themselves. I'm trying to learn the basic concepts in layman terms or you can say in 'pop science' fashion. I hope you don't mind it. Thanks!
My apologies, Sir, that I couldn't frame the question properly but I made an honest attempt. But I hope now you understand what I was trying to say and the point I was trying to make.
So, finally, it's concluded that Newtonians would be see that more fuel has been consumed than was originally calculated. The mass increase during the trip was real. In their attempt to understand this difference, they will try to find an explanation. I wanted to clarify three more related points.

Question 1:
There is still one point which bothers me. During the trip, the pilot cannot know if local time has been dilated compared to that of the Earth and also he cannot find that mass of rocket has increased but he can definitely see the gauge and see that more fuel is being consumed than was calculated. Would the pilot be able to notice the difference?
Thank you!

Let's do a practical example. Assume your rocket was accelerating at a proper acceleration of 10m/s, to a velocity relative to the Earth of 0.99c.
If we were to use Newtonian physics, then, you would simply divide the final speed by the acceleration to get the time needed according to both Earth and pilot, this works out to be ~0.94 yrs.
However, by Relativity these times would be ~6.7 yrs for the Earth, and 2.52 yrs for the pilot.
For the pilot, he isn't burning fuel at any greater rate than he would to maintain the same proper acceleration as he would according to Newton, but he does have to burn fuel for a longer time in order to reach 0.99c relative to the Earth.
The reason being that velocities do not add up the same way in Relativity as they do according to Newton.
With Newton, your relative speed increases linearly with time. After 1 sec, you are moving at 10 m/sec, after 2 sec, 10 m/sec etc. By counting the number of seconds you've been accelerating and adding 10 m/s for each one (10 m/s+10m/sec+10m/sec...) you'll end up with your final velocity relative to the Earth.
However, under Relativity, velocities don't add up linearly, but by the rule:
w=(u+v)/(1+uv/c^2), were u and v are the added velocities.
At velocities that are small compared to c, these answers are almost exactly the same as when you add them directly, but begin to differ significantly as you approach c.
If u and v were both 0.1c, then the resultant velocity would be 0.198c, or just a tad under the 0.2c you expect under Newton.
If u= 0.89c and v= 0.1 c, the result is ~0.91c, A gain of just 0.02c, instead of 0.1c
For our pilot, each successive sec of acceleration adds a smaller amount to his velocity relative to the Earth than the previous sec did.
So even though the pilot is feeding fuel to the rocket at a rate, that for him, produces a constant acceleration of 10m/s, his velocity relative to the Earth doesn't build up as fast as he would expect using Newtonian physics, and he has to burn his engines longer and end up using fuel to get up to 0.99c then Newton predicted.
For the Earth, he will be burning his engines for even longer. But, also according to the Earth, as he picks up speed, his rocket undergoes time dilation and thus burns fuel at a slower and slower rate. The combination of longer total time, and the decreasing rate of fuel consumption, produces the same answer as to total fuel used to reach 0.99c

 

[PeroK]

For the Earth, he will be burning his engines for even longer. But, also according to the Earth, as he picks up speed, his rocket undergoes time dilation and thus burns fuel at a slower and slower rate. The combination of longer total time, and the decreasing rate of fuel consumption, produces the same answer as to total fuel used to reach 0.99c

... I guess you mean the same answer for final fuel consumption as measured on the ship?

 

[Janus]

... I guess you mean the same answer for final fuel consumption as measured on the ship?

Yes.

 

[PeterDonis]

if you've defined "kind of thing, physically" as whether or not a thing is invariant.

That is one way of distinguishing kinds of things physically, yes. It's not the only way, but it certainly is a way.

it highlights that there's obviously a sense in which "rest energy" and "total energy" can be regarded as the "same kind of thing, physically": in any inertial frame, $E = E_0 + E_k = \gamma E_0$.

Your labeling obfuscates the physical nature of the things. Nobody measures $E_0$ by measuring energy. They measure it by measuring mass. Whereas $E_k$ is measured by measuring energy--for example, the amount of work that can be done by bringing the object to rest in a controlled fashion. And nobody measures $\gamma E_0$ at all; it's calculated.

 

[PAllen]

...
@PeterDonis suggested calling coordinate time something else
...

I instinctively disagree—strongly—that this would help beginners, but it's a bold and thought-provoking perspective.

How about an even more radical concept (I do not think it would help beginners, but could be introduced reasonably early to undermine over interpreting coordinate quantities):

Use only Dirac all lightlike coordinates e.g. u and v, both lightlike . The SR metric becomes:

ds² = 2 dudv

This can be readily generalized to 4 lightlike coordinates.

Then the student is force to deal with space and time using only invariant procedures, as the coordinates say nothing directly about space or time.

 

[SiennaTheGr8]

Your labeling obfuscates the physical nature of the things.

I think $E = E_0 + E_k = \gamma E_0$ better elucidates the nature of the things than $E = mc^2 + E_k = \gamma mc^2$ does.

Nobody measures $E_0$ by measuring energy. They measure it by measuring mass. Whereas $E_k$ is measured by measuring energy--for example, the amount of work that can be done by bringing the object to rest in a controlled fashion. And nobody measures $\gamma E_0$ at all; it's calculated.

First, I disagree with the notion that how one goes about measuring or calculating these quantities is tantamount to "the physical nature of the things" or should determine what symbols and words we use for them (if that's what you're suggesting).

Second, measuring mass is measuring the energy in the rest frame! Yes, for practical reasons we're more or less constrained to measuring it "externally" (by which I mean a force-over-acceleration or density-times-volume kind of deal), but the thing that's being measured is the sum of all the "internal" energy-contributions. The "mass" doesn't have an independent existence beyond that.

Or is your point that our scales use (say) kilograms rather than... (consults Wolfram Alpha)... exajoules? petajoules? I don't think that's what you're getting at, but if so, that's just part of the convention I'm criticizing.

 

[SiennaTheGr8]

How about an even more radical concept (I do not think it would help beginners, but could be introduced reasonably early to undermine over interpreting coordinate quantities):

Use only Dirac all lightlike coordinates e.g. u and v, both lightlike . The SR metric becomes:

ds² = 2 dudv

This can be readily generalized to 4 lightlike coordinates.

Then the student is force to deal with space and time using only invariant procedures, as the coordinates say nothing directly about space or time.

 

[SiennaTheGr8]

Kidding aside, does anyone have a good resource on lightlike coordinates?

 

[PAllen]

Kidding aside, does anyone have a good resource on lightlike coordinates?

I have a draft insight I've been sitting on forever on them. Maybe, with this nudge, I'll finally polish it up and publish it. It deals with 2, 3, and 4 dimensional cases, showing how to identify that a metric like the Dirac is nothing by flat Minkowski space, and how to easily generate a family coordinate transforms between standard inertial coordinates and all lightlike coordinates to achieve a given metric form. A twist is that for the 2 dimension case, a form like 2 dudv is ambiguous as to signature (it can be achieved from a metric expressed in either signature). However, for 3 or 4 dimensions, there is no ambiguity. A metric with all positive off diagonal components (and all zero diagonal components) unambiguously has signature with (+,-,-,), which is surprising at first glance.

 

[SiennaTheGr8]

I have a draft insight I've been sitting on forever on them. Maybe, with this nudge, I'll finally polish it up and publish it.

Look forward to reading it when you do.

 

[PeterDonis]

I think $E = E_0 + E_k = \gamma E_0$ better elucidates the nature of the things than $E = mc^2 + E_k = \gamma mc^2$ does.

Well, then we have a disagreement about pedagogy. I understand such disagreements are fairly common.

I disagree with the notion that how one goes about measuring or calculating these quantities is tantamount to "the physical nature of the things"

I'm not sure why. Ultimately all of physics has to come down to actual measurements we make. The measurements and their results are the bedrock of our understanding. That's how we find out "the physical nature of things"--by making measurements and doing experiments.

measuring mass is measuring the energy in the rest frame!

No, it isn't. You don't measure energy on a balance. To measure the energy corresponding to the rest mass of something, you would have to find a way to convert that rest mass into energy, i.e., something that can do work. A mass sitting at rest can't do any work.

the thing that's being measured is the sum of all the "internal" energy-contributions. The "mass" doesn't have an independent existence beyond that.

As far as particle physics is concerned, that's an open question; we don't fully understand how mass arises at the fundamental level so we can't say for sure that it all ends up being some kind of internal energy of stuff that has no intrinsic rest mass.

If you're talking about macroscopic objects, without inquiring into their fundamental constituents, what you say is simply false. We don't have any macroscopic objects made solely of radiation (i.e., "stuff" with zero rest mass), which is what they would have to be for your claim to be true of them as you state it.

s your point that our scales use (say) kilograms rather than... (consults Wolfram Alpha)... exajoules?

No, my point is that the devices we use to measure mass, like balances, are different physical devices from the devices we use to measure energy. That has nothing to do with your choice of units. You could label the test masses you use in your balance in GeV for all I care; you're still using a balance instead of measuring capacity to do work.

 

[PainterGuy]

Thank you, @PeroK, @Ibix, @Nugatory, and @Janus.

I'd try to wrap up this discussion as it has been advised to follow a properly structured source to learn the theory. I hope it'd okay if I ask some related questions and make some comments.

For the Earth, he will be burning his engines for even longer. But, also according to the Earth, as he picks up speed, his rocket undergoes time dilation and thus burns fuel at a slower and slower rate. The combination of longer total time, and the decreasing rate of fuel consumption, produces the same answer as to total fuel used to reach 0.99c

Okay. The fuel consumed according to an Earth observer and the pilot is the same, and the rocket's fuel gauge would verify this result. But according to Newtonian calculation more fuel has been consumed. Do you agree with this?We can say that the rocket clock runs fine for the pilot but it's running slow, i.e. time dilated, according to an Earth observer. But at the same time, the pilot finds that the Earth clock is running slower compared to the rocket clock. At the end of day, it would be pilot's clock which was actually running slower. One can say that why an Earth observer's clock is more 'real' than the pilot's, I'd say it's so because at the end of day we observe the universe through Earth's frame of reference or similar frame of reference. So, the pilot experienced a 'temporary illusion' and if the pilot was destined to spend most part of the life from birth to death aboard the rocket then his/her Earth time would be an 'illusion'.

My original question from post #1, Question 1, about a GPS satellite is related here. The satellite clock gets ahead of the Earth clock by 45 microseconds per day. For an Earth observer the satellite clock suffers time contraction but for the satellite observer it's Earth clock which undergoes time dilation. (I hope I'm saying it correctly). But, again, at the end of day, it's the satellite clock which is running faster or has been time contracted.From what I have read (my apologies if I'm not putting it together properly), Einstein originally didn't use the concept of spacetime for his theory in 1905. It was actually Minkowski who gave Einstein's theory a geometric interpretation in terms of four dimensional spacetime. Initially, Einstein didn't like this spacetime interpretation too much but later he adopted it and it was one of the factors along with his desire to incorporate non-inertial frames of reference into his 1905 theory which motivated him to come up with the theory of general relativity. There is a good related discussion here: https://hsm.stackexchange.com/quest...minkowski-spacetime-before-special-relativity

Thanks a lot, as always!

 

[Nugatory]

But according to Newtonian calculation more fuel has been consumed. Do you agree with this?

Sure. The Newtonian calculation is wrong, and it turns out that in this particular example the incorrect result of this incorrect calculation is lower than the correct answer. But there’s nothing especially surprising about an incorrect calculation producing an incorrect answer. Thinking about the Newtonian answer makes about as much sense as thinking about the results you’d get from using a defective calculator - if your calculator doesn’t do arithmetic right you don’t try to explain the fuel consumption using numbers from that calculator, you throw it out and get one that does do arithmetic right.

At the end of day, it would be pilot's clock which was actually running slower.

If you choose to analyze the problem using a frame in which the Earth is at rest, and if we bring the traveler to rest in that frame at the end of journey, and we use the most natural simultaneity convention in that frame to check the two clock readings at the same time so we can see which one is ahead of the other... then yes, the ship clock will have lost some time compared to the Earth clock.

However, that’s a lot of qualifiers. If we use a frame in which the Earth is not at rest (a reasonable choice for anyone who has noticed that the Earth is orbiting the sun, the sun is orbiting the galactic center, and the entire galaxy is moving through intergalactic space) we could easily find that it’s the Earth clock that is behind. Thus...

One can say that why an Earth observer's clock is more 'real' than the pilot's. I’d say it's so because at the end of day we observe the universe through Earth's frame of reference or similar frame of reference

Only if you’re willing to insist that there’s something special about the frame in which the Earth is at rest. “Some similar frame” won’t necessarily produce the same result. (And have you followed the advice earlier in this thread to look at the relativity of simultaneity? You have to understand that before you can make any conclusions about clocks that are not at the the same place at the same time).

 

[Janus]

Thank you, @PeroK, @Ibix, @Nugatory, and @Janus.

I'd try to wrap up this discussion as it has been advised to follow a properly structured source to learn the theory. I hope it'd okay if I ask some related questions and make some comments.
Okay. The fuel consumed according to an Earth observer and the pilot is the same, and the rocket's fuel gauge would verify this result. But according to Newtonian calculation more fuel has been consumed. Do you agree with this?

If you are measuring amount of fuel needed to reach a given velocity, then yes, Relativity predicts you will use more fuel. But, as pointed out by @Nugatory, in our universe, Newtonian physics give you the wrong answer.
However, if you consider things in terms of fuel used for distance traveled, you get a different result. Accelerating at 10 m/s for .95 yrs by Newtonian rules will get you ~0.47 ly from the Earth and moving at 0.99c.
Accelerating at 10m/s for 2.52 yrs ship time, will also get you up to 0.99c, but 5.8 ly from Earth (measured in the Earth frame). So, while you have burned 2.65 times as much fuel, you've gone 12.3 times further from the Earth. In order for you to get 5.8 ly from the Earth accelerating under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time) So if I wanted to get to the nearest star in the shortest amount of ship time, while using less fuel, Relativity is my friend.

We can say that the rocket clock runs fine for the pilot but it's running slow, i.e. time dilated, according to an Earth observer. But at the same time, the pilot finds that the Earth clock is running slower compared to the rocket clock. At the end of day, it would be pilot's clock which was actually running slower. One can say that why an Earth observer's clock is more 'real' than the pilot's, I'd say it's so because at the end of day we observe the universe through Earth's frame of reference or similar frame of reference. So, the pilot experienced a 'temporary illusion' and if the pilot was destined to spend most part of the life from birth to death aboard the rocket then his/her Earth time would be an 'illusion'.

The fact that the pilot measures the Earth clock running slow compared to his is no less real than the fact that the Earth measures his clock running slow. Observing the universe "through Earth's frame of reference" is a convenience for us, and does not establish a universal time frame. Someone in a frame moving at 0.8c relative to the Earth is just as entitled to observe the universe from his frame. If the pilot lives out his whole life in that ship without ever slowing down relative to the Earth, then for him, the Earth really does age less than he does during his life.
If the pilot goes out and then returns, then yes, he will find that he has aged in total less than the Earth has. And while as far as the Earth frame is concerned, this is all due to time dilation, this is not the case for the pilot. For him, the Earth spent a good chunk of his trip aging slower than him( during the outbound and return legs of the trip), and it was only during that period when he was accelerating in order to reverse direction back towards the Earth that the Earth aged faster. His view of Earth aging slow, Earth aging fast, Earth aging slow, is just as valid as the Earth's view of him just aging slow. From another frame, The Earth could have run slow the whole time, while the pilot aged normally for the first half of the trip, and then aged much more slowly than the Earth for the second half, still resulting in less total accumulated time for the pilot than the Earth. There is no one right frame which is the one that actually reflects what is happening.

My original question from post #1, Question 1, about a GPS satellite is related here. The satellite clock gets ahead of the Earth clock by 45 microseconds per day. For an Earth observer the satellite clock suffers time contraction but for the satellite observer it's Earth clock which undergoes time dilation. (I hope I'm saying it correctly). But, again, at the end of day, it's the satellite clock which is running faster or has been time contracted.

No. For the GPS satellite, things are different than that of someone traveling in a straight line relative to the Earth. For now, we will ignore the gravitational time dilation effect, and for argument's sake assume no gravity at all. Just considering the SR effect. The GPS satellite is orbiting the Earth, and thus is traveling in a circle. It is undergoing a centripetal acceleration. This acceleration effects how it measures Earth time, just like the acceleration the pilot underwent during turnaround effected his. So, if yo place a clock circling around another at 0.866c, The central clock will measure the circling clock as ticking 1/2 as fast. The circling clock, will, due to the centripetal acceleration it is under, measure the central clock as ticking twice as fast as itself. The two clocks will agree that the circling clock is the one running slow.
This is what occurs with GPS clocks, If it were just a matter of dealing with the circular motion of the satellite, both surface and satellite would say that the satellite clock runs slower. However once we reintroduce gravity, Gravitational time dilation becomes the stronger effect, and has the GPS clock ticking faster as a whole, with both surface and satellite agreeing as to the magnitude of the difference.

 

[SiennaTheGr8]

No, it isn't. You don't measure energy on a balance. To measure the energy corresponding to the rest mass of something, you would have to find a way to convert that rest mass into energy, i.e., something that can do work. A mass sitting at rest can't do any work.

As far as particle physics is concerned, that's an open question; we don't fully understand how mass arises at the fundamental level so we can't say for sure that it all ends up being some kind of internal energy of stuff that has no intrinsic rest mass.

If you're talking about macroscopic objects, without inquiring into their fundamental constituents, what you say is simply false. We don't have any macroscopic objects made solely of radiation (i.e., "stuff" with zero rest mass), which is what they would have to be for your claim to be true of them as you state it.

Sure, I should have included the caveat that elementary particles presumably have "intrinsic" rest-energy.

But for a system that's more than an elementary particle, its mass is the sum of the "internal" energy-contributions: that is, the rest-energies of the constituent particles, the particles' kinetic energies (as measured in the system's center-of-momentum frame), and the potential energy associated with the constituents' relative positions (defined as negative for attractive forces and positive for repulsive forces, and with the "zero point" corresponding to the limit where the constituents are infinitely far from each other).

So measuring an object's rest energy (mass) is indeed measuring the sum of its "internal" energy-contributions. The equivalence of mass and rest energy is a hard equivalence. Any statement one might make about a thing's "mass" is nothing more and nothing less than a statement about its "Energieinhalt."

Accordingly, "mass" can't be "converted" into energy because it already is energy (and to be clear, I'm using "energy" here to refer generically to the additive-and-conserved quantity, not as shorthand for an object's "total energy"; language is slippery). Rather, there are physical processes that can convert rest energy into other forms of energy. For a composite system, this often entails the conversion of some of the "internal" potential energy into the kinetic energy of some of the object's constituents, but of course even the "annihilation" of fundamental particles is possible. And if you want to use the "ability to do work" definition of energy, then I'd counter that the rest energy ("mass") of an object sitting on a scale is precisely a measure of the maximum amount of work that the object could do if those aforementioned physical processes went to town on it.

 

[PeterDonis]

I should have included the caveat that elementary particles presumably have "intrinsic" rest-energy.

No, they have intrinsic rest mass (or invariant mass)--at least, as far as we know some of them do. (Some, like photons and gluons, don't.)

But you can't just help yourself to the assumption that those intrinsic rest masses count as energies; that's precisely the point at issue.

for a system that's more than an elementary particle, its mass is the sum of the "internal" energy-contributions: that is, the rest-energies of the constituent particles

You're assuming your conclusion. If rest mass does not count as internal energy for constituent particles (which, as above, you can't assume it does), then rest mass of a composite system is not just the sum of the internal energy contributions.

The rest of your post simply makes the same assumption without argument.

I don't see the point of arguing about this further. We have a difference of opinion about terminology which I don't think is going to be resolved. As long as we each understand the terminology the other is using, we can still communicate about the physics.

 

[SiennaTheGr8]

I don't see the point of arguing about this further. We have a difference of opinion about terminology which I don't think is going to be resolved. As long as we each understand the terminology the other is using, we can still communicate about the physics.

Agreed. Thanks, Peter.

 

[PainterGuy]

Thank you very much!

Now please bear with me.

Only if you’re willing to insist that there’s something special about the frame in which the Earth is at rest. “Some similar frame” won’t necessarily produce the same result. (And have you followed the advice earlier in this thread to look at the relativity of simultaneity? You have to understand that before you can make any conclusions about clocks that are not at the the same place at the same time).

Yes, I personally prefer Earth's frame of reference because it seems more natural and as a novice it seems to help understand it better.

Yes, I did watch a video about "Einstein train simultaneity". This one: youtube.com/watch?v=wteiuxyqtoM

However, if you consider things in terms of fuel used for distance traveled, you get a different result. Accelerating at 10 m/s for .95 yrs by Newtonian rules will get you ~0.47 ly from the Earth and moving at 0.99c.
Accelerating at 10m/s for 2.52 yrs ship time, will also get you up to 0.99c, but 5.8 ly from Earth (measured in the Earth frame). So, while you have burned 2.65 times as much fuel, you've gone 12.3 times further from the Earth. In order for you to get 5.8 ly from the Earth accelerating under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time) So if I wanted to get to the nearest star in the shortest amount of ship time, while using less fuel, Relativity is my friend.

I'm sorry but I'm confused and my head hurts. "2.52 yrs ship time" is dilated according to the reference frame of earth. Therefore, I think, "3.3 yrs" won't be different from "2.52 yrs ship time" once the pilot completes his mission and his mission's duration is checked using Earth's clock; or in other words once the ship time is converted into Earth time using proper factor, it would be same as 3.3 yrs.

"under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time)" - In other words, yes, it would take a Newtonian longer because your clock was running slow. But I don't see how a Newtonian would need to spend more fuel, especially when Newtonian rocket doesn't 'suffer' from any relativistic mass effect, informally speaking, its mass doesn't increase.

Once again, I don't understand why it'd take "30% more fuel" according to Newtonian calculation; in post #53, https://www.physicsforums.com/threa...mass-and-fuel-consumption.984366/post-6299827, @Nugatory confirmed that a Newtonian would say that more fuel has been consumed because Newtonian antiquated model doesn't take into account relativistic effects of mass as it moves.

I understand that the special relativity models the nature more accurately but I'm looking at it from perspective of Newtonian antiquated model. I'm also not focusing on spacetime because even Einstein himself didn't really consider it when he came up with the special theory of relativity. I'm ignoring the general relativity at this stage. Newtonian model uses fixed flow of time and no distinction between rest mass and moving mass.

For him, the Earth spent a good chunk of his trip aging slower than him( during the outbound and return legs of the trip), and it was only during that period when he was accelerating in order to reverse direction back towards the Earth that the Earth aged faster. His view of Earth aging slow, Earth aging fast, Earth aging slow, is just as valid as the Earth's view of him just aging slow.

I googled the effects of acceleration on time and found few things which I didn't know before. I had thought that only when you move fast with respect to an inertial frame, your time gets slow down, i.e. dilated. It looks like acceleration also affects the time in a different manner; I hope it's not a consequence of general relativity because I'm only focusing on special relativity. The theory of general relativity models the acceleration as gravity .

For example, have a look below on the quote. My apologies if it's not entirely accurately but I needed your guidance if it's correct. For example, if a rocket is moving away from Earth to some other planet B. The rocket clock appears to slow down with respect to an Earth observer but a rocket observer notices Earth's clock slowing down. If the rocket is headed directly toward planet B, how would the rocket observer see planet B's clock and how rocket clock appears to planet B observer? I'm assuming rocket is traveling at constant velocity.

According to what is said below, as the rocket accelerates the rocket observer sees Earth clock slowing down more but sees planet B clock moving faster. Is it correct?

"Moving fast only. Actually, just moving at all, though you won't notice it much at low speeds.

Acceleration causes another time effect, which seems different but drops out of the same math. Clocks "above" you, or in the forward direction of acceleration, tick faster. Clocks "below" you tick slower. This happens even when you're rigidly attached to the clock, and both you and the clock are accelerated."
Source: https://qr.ae/T3zzwJ

Well, if you think I'm making no sense then I'd understand if you don't comment.This is an addition to what I said earlier towards the end of my last post.
"In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in the theory of relativity. Philosophers sometimes treat the philosophy of space and time as if it were a mere appendix to Minkowski’s theory. In this critical study, Joseph Cosgrove subjects the concept of spacetime to a comprehensive examination and concludes that Einstein’s initial assessment of Minkowksi was essentially correct."
Source: https://www.palgrave.com/gp/book/9783319726304#aboutBookThe following part is my personal view and I also attempt to explain why I'm finding the special theory of relativity difficult.

As another example, let's consider a thought experiment. If you are asked to go around the Earth at 0.9c speed for one second using fixed amount of fuel. Let's ignore the air friction, gravity, and suppose the rocket starts and end its journey at 0.9c without any acceleration, also ignore centripetal acceleration. The speed of light is 300000 km/s and circumference of Earth is 40075 km. Using Newtonian calculation, in one second you should be able to go around the Earth 6.74 times. A Newtonian standing on Earth would see the rocket going slow, length contracted in the direction of travel but I don't think the Newtonian would be able to notice that the rocket has become more massive. Therefore, after one second the Newtonian would clearly see that the rocket hasn't circled the Earth 6.74 times. If the rocket is taken down once Newtonian clock ticks one second, it would also be noticed that for whatever amount of journey it has covered (which is clearly going to be less than 6.74 times Earth circumference), it has consumed more fuel as it should. Forget what the pilot of rocket has to say about it. Do I make any sense?

Also, for example, in the example shown in the video mentioned above about simultanety, youtube.com/watch?v=wteiuxyqtoM , if there were two light sensors at the ends of train, the person on train would also agree that both flashes occurred at the same time. Yes, if the train is some kind of planet and there was no way of communicating with a person situated outside somewhere above that planet, then the conclusion of person riding the 'train/planet' would be acceptable. Perhaps, the example is a bad example but online tutorials are full of such examples.

In my humble view, the theory of special relativity, is presented more like pure math rather than applied math. Personally, I have nothing against pure math but applied math seems more interesting although the very foundation of applied math is in fact the pure math. I have been looking for a book which presents theories of relativity, especially special relativity, more from 'human' and 'physical' perspective but no success. I will elaborate on it below.

A cathode ray tube takes into account of relativistic effects on length and mass of electrons. An electron has length contraction, time dilation, and its inertial mass increases. I wouldn't really care how I appear to the electron - if it sees me length contracted unicorn or alien then that's not my problem :). Most important to me, as a novice, is to understand how an electron looks as it travels at very high speed. I can imagine later, how the world appears to an electron if it were a living being!

"Cathode ray tube (CRT) televisions create pictures by shooting electrons at a phosphorous screen. These electrons are accelerated to high velocities, near 20- 30% of the speed of light. Remember from special relativity that as a particle approaches speeds near light speed, the energy required to propel the particle is increased. Magnets in the television are responsible for placing the electrons in the correct configuration on the screen. They must account for the relativistic effects on these electrons or the picture created will be out of focus (Akpan, 2015)". Source: https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1071&context=tdr "These electrons are moving at roughly a third of the speed of light. This means that engineers had to account for length contraction when designing the magnets that directed the electrons to form an image on the screen. Without accounting for these effects, the electron beam's aim would be off and create unintelligible images." Source: https://www.iflscience.com/physics/4-examples-relativity-everyday-life/amp.html, https://www.quora.com/Is-length-con...chard-Muller-3?ch=12&share=c5c2c623&srid=gk8x . The same goes for the ladder paradox, https://en.wikipedia.org/wiki/Ladder_paradox, if I build a barn and let the ladder move through it at really fast speed, then it's the ladder which contracts in my physical world. The ladder is in my world or the world of barn and ultimately the ladder's movement is not permanent, it has to stop ultimately.

As an another example, the guy gives a very nice introduction to special theory of relativity 'from human point of view', youtube.com/watch?v=umLcFAI5SZg . He won $400000 award for it as well.

Helpful links:
1: http://web.pdx.edu/~egertonr/ph311-12/relativ.htm
2: http://www.exo.net/~pauld/activities/physics/relativitytelevision.htm
3: https://www.iflscience.com/physics/4-examples-relativity-everyday-life/amp.html
4: youtube.com/watch?v=mnJuKXhFaQ8
5: https://physics.stackexchange.com/q...he-speed-of-light-vary-in-non-inertial-frames
6: http://www.alternativephysics.org/book/MuonRelativity.htm
7: https://physics.stackexchange.com/q...ncy-of-speed-of-light-in-gr?noredirect=1&lq=1

 

[jbriggs444]

I googled the effects of acceleration on time and found few things which I didn't know before. I had thought that only when you move fast with respect to an inertial frame, your time gets slow down, i.e. dilated. It looks like acceleration also affects the time in a different manner; I hope it's not a consequence of general relativity because I'm only focusing on special relativity. The theory of general relativity models the acceleration as gravity.

It is an effect seen in general relativity. It is also an effect that can be seen in special relativity if one adopts a particular type of accelerating coordinate system, Rindler coordinates.

If you restrict your attention to inertial frames in special relativity then no such effect exists.

For example, have a look below on the quote. My apologies if it's not entirely accurately but I needed your guidance if it's correct. For example, if a rocket is moving away from Earth to some other planet B. The rocket clock appears to slow down with respect to an Earth observer but a rocket observer notices Earth's clock slowing down. If the rocket is headed directly toward planet B, how would the rocket observer see planet B's clock and how rocket clock appears to planet B observer? I'm assuming rocket is traveling at constant velocity.

According to what is said below, as the rocket accelerates the rocket observer sees Earth clock slowing down more but sees planet B clock moving faster. Is it correct?

"Moving fast only. Actually, just moving at all, though you won't notice it much at low speeds.

Acceleration causes another time effect, which seems different but drops out of the same math. Clocks "above" you, or in the forward direction of acceleration, tick faster. Clocks "below" you tick slower. This happens even when you're rigidly attached to the clock, and both you and the clock are accelerated."
Source: https://qr.ae/T3zzwJ

The writer there is adopting an accelerating coordinate system. You can think about an accelerating coordinate system (one particular accelerating coordinate system anyway) as a sequence of inertial frames anchored to a uniformly accelerating object. Each inertial frame in the sequence is obviously moving slightly faster than the last. Suppose that lay a coordinate system down on this frame. You have two clocks whose relative tick rates you want to consider. The clocks are at some distance from one another in the direction of the acceleration. Each time you change inertial frames, you change relativity of simultaneity. That leads to an asymmetry in the calculated relative rates of the two clocks.

Using accelerated coordinate systems does not do anything physical, of course. Coordinate systems are just doodles on pieces of paper. Doodles cannot do anything physical.

 

[PeroK]

@PainterGuy you are wasting your time on Quora. Unless you already understanding the subject it's impossible to sort the good answers from the nonsense.

Why not give Morin's book a try?