# Why is the Equivalence Principle True?

## Main Question or Discussion Point

The equivalence principle states that an accelerating observer who has no external information (view of fixed stars, etc) can in principle not perform an experiment to determine whether he is either undergoing linear acceleration or at rest in a gravitational field. This leads to the equivalence of inertial and gravitational mass.

Is there an underlying reason this should, or could, be true? For instance (feel free to offer corrections...) the higgs field only couples to certain particles involved in the weak nuclear force, and in this case only causes them to have an inertial mass. The equivalence of inertial and gravitational mass is just purely a postulate.

I know this is one of those statements that appears obvious, but what is the deeper reasoning behind it?

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Dale
Mentor
The equivalence of inertial and gravitational mass is just purely a postulate.
That is correct, it is a postulate. It is accepted because the theory based on that postulate agrees with experiments performed to date, which is the only scientific criterion for accepting or rejecting a postulate.

I smell an alternative theory incoming. ia, are you aware of how much in SR/GR and QM is conjecture and postulate? If not, fair enough, now you know. If so... then why bring this up if not to offer your alternative. Given your "timeless universe" from the 3+1 thread, I'm really looking forward to this.

As for "deeper reasoning", you want the reasoning behind... Equivalence? The Higgs Mechanism? Spontaneous Gauge Symmetry Breaking in general? You've raised all of these, and seem directionless in terms of what reasoning you're searching for. It seems to me you want a preview of the LHC at full power.

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Dale
Mentor
It seems to me you want a preview of the LHC at full power.
Oooh, I want that too!

Oooh, I want that too!
Oh god, me too... :rofl:

EDIT: Just thinking about the amount of data produced by that monster makes me weak in the knees. Now easy mit that crygoenic Helium boys!

I smell an alternative theory incoming. ia, are you aware of how much in SR/GR and QM is conjecture and postulate? If not, fair enough, now you know. If so... then why bring this up if not to offer your alternative. Given your "timeless universe" from the 3+1 thread, I'm really looking forward to this.

As for "deeper reasoning", you want the reasoning behind... Equivalence? The Higgs Mechanism? Spontaneous Gauge Symmetry Breaking in general? You've raised all of these, and seem directionless in terms of what reasoning you're searching for. It seems to me you want a preview of the LHC at full power.
Please just stop replying to my posts by trolling. All I expressed in the other post was a shortened version of what 3 or 4 physics professors choose to write about in the fxqi essay contest. If you're taking issue with the content of what I typed, you're taking issue with what they wrote, because all I did was attempt to relay it in about a paragraph.

I'm asking an honest question here. Everyone knows the equivalence principle is experimentally true, and that it's used to relate inertial and gravitational mass. What I'm asking is if anyone has any further insight into it's development, other things it relates to, etc, because I know I don't, and it's an interesting topic. If you don't have anything to add about the topic, then please stop replying.

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Please just stop replying to my posts by trolling. All I expressed in the other post was a shortened version of what 3 or 4 physics professors choose to write about in the fxqi essay contest. If you're taking issue with the content of what I typed, you're taking issue with what they wrote, because all I did was attempt to relay it in about a paragraph.

I'm asking an honest question here. Everyone knows the equivalence principle is experimentally true, and that it's used to relate inertial and gravitational mass. What I'm asking is if anyone has any further insight into it's development, other things it relates to, etc, because I know I don't, and it's an interesting topic. If you don't have anything to add about the topic, then please stop replying.
Please stop questioning basic principles of physics based on a Nature Essay Contest.

ia said:
I'm asking an honest question here. Everyone knows the equivalence principle is experimentally true, and that it's used to relate inertial and gravitational mass. What I'm asking is if anyone has any further insight into it's development, other things it relates to, etc, because I know I don't, and it's an interesting topic. If you don't have anything to add about the topic, then please stop replying.
It's an interesting topic for me also ia. The equivalence principle is only true to the degree of accuracy that it has been tested. Which concept of gravitational mass are you referring to, active or passive? What do you mean by "further insight into it's development"?

It's an interesting topic for me also ia. The equivalence principle is only true to the degree of accuracy that it has been tested. Which concept of gravitational mass are you referring to, active or passive? What do you mean by "further insight into it's development"?
It is only VERIFIED to the degree of accuracy to which it has been tested, truth is another matter. Then again, that's true of any theory, conjecture, hypothesis, and postulate!

It is my experience that questions such as "Why is 'N' principle/conjecture/etc true" usually leads to an endless cycle of "why's".

The EP is NOT true, it is a postulate which is PROBABLY an accurate description or approximation. The basis upon which ia's query is set forth is flawed, and asks a question which has no answer other than what DaleSpam gave him: It's a postulate, not a truth, and it is accepted for all of the reasons you could find on Wikipedia, google, or a textbook.

Dale
Mentor
I agree with Frame Dragger. I don't like to use the word "true" to describe any scientific theory, principle, or postulate. I prefer to use the words "verified" or "falsified" as they have much more specific and correct meaning.

Semantics: It isn't pretty, but someone has to be about it!

I find when it comes to any science, it's important to respect the terminology so that more semantic arguments are avoided. That, and as DaleSpam said, it's just not the case that any theory is "true"... at least, not that any person could know. In fact, that's not even a realistic goal set by professionals in the field. Truth is the realm of Philosophy, and I find it telling that we're being asked a philosophical question: "Why...?".

The answer as always: "Who the **** knows?!".

Physics is about WHAT, and HOW, and "Why" only enters the equation when it leads to more fundamental physical principles. If you're aiming for something more... that'd be METAphysics.

Physics isn't physics if we're not talking about experimental principles that can be tested in some fashion. That may be a fine pursuit, just not in the Relativity forum of PF.

ia said:
True can roughly be taken to mean correct to within experimental limits. Anyway, this is pointless. Congratulations.
Well, at least you're in this for the long haul. Maybe you could actually LEARN from this?

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To 'prove' the equivalence principle would be a great achievement, so naturally it is a task which attracts many people, including the ZPF claque, who want to explain everything using the ZPF. Drs Rueda, Haisch and Puthoff do claim they have made progress in this area by explaining inertia as a drag force created by the ZPF, and the cause of gravity some kind of field cancellation caused by Matter/ZPF interaction. A 'common cause' argument.

These theories have been around for a decade and seem to have gone up like a lead balloon. FrameDragger, since you like way-out theories, this may provide some amusement.

I thought this was worth mentioning because

(a) it might explain the OP's motive in asking

(b) if not (a), at least he's got something he can look at, even if it is wildly speculative,

To 'prove' the equivalence principle would be a great achievement, so naturally it is a task which attracts many people, including the ZPF claque, who want to explain everything using the ZPF. Drs Rueda, Haisch and Puthoff do claim they have made progress in this area by explaining inertia as a drag force created by the ZPF, and the cause of gravity some kind of field cancellation caused by Matter/ZPF interaction. A 'common cause' argument.

These theories have been around for a decade and seem to have gone up like a lead balloon. FrameDragger, since you like way-out theories, this may provide some amusement.

I thought this was worth mentioning because

(a) it might explain the OP's motive in asking

(b) if not (a), at least he's got something he can look at, even if it is wildly speculative,
Dragging in the ZPF... Oh that is priceless! :rofl: Mentz, you're a mensch.

Is there an underlying reason this should, or could, be true? For instance (feel free to offer corrections...) the higgs field only couples to certain particles involved in the weak nuclear force, and in this case only causes them to have an inertial mass. The equivalence of inertial and gravitational mass is just purely a postulate.
Not that you are saying otherwise, but just to make sure let me state: the Higgs isn't the cause of inertial mass. For example, the vast majority of our mass is from the nuclei in atoms, and those in turn get their rest energy from strong color interactions, and the electromagnetic interaction, etc. Very little of our mass is actually due to interactions with the Higgs field.

The best I can do to give better insight into "Why the equivalence principle?" is to comment on it a bit further than what you introduced it as above.

Pause a bit to realize the amazing property of SR, which describes flat spacetime. Despite describing the "stage" the physics will play on, it puts strong restrictions and requirements on the physics. Somehow in describing just the "background", the "stage", essential parts of the physics are already included.

Now move onto GR, which can handle general spacetimes. In some sense, the equivalence principle comes from the fact that the gravity comes from only coupling to a constant and the total stress energy tensor. This makes it completely ambivalent to what is causing the stress energy tensor. We can include anything and it doesn't matter, GR says the coupling will be to the total stress energy tensor. What is strange is, again like SR, general relativity in describing the "stage" goes beyond just describing gravity and is somehow able to put restrictions on what the physics can do. The interactions can't depend directly on the local Weyl curvature for some reason ... so the equivalence principle holds.

I find that amazing. In describing the stage, bizarrely the physics plops out. In Quantum field theory, this goes even a bit further. If you consider spacetime to also have a local U(1) symmetry degree of freedom ... bam, electrodynamics fall out. Assume a local symmetry / degree of freedom and an interaction pops out (another example SU(3) -> the color interaction).

Now, starting to get into what you may be looking for. What if we try to consider a spin 3/2 or spin 2 particle? People have tried to write things down like extensions of the dirac or klein-gordon for higher spin and weird inconsistencies pop up ( http://en.wikipedia.org/wiki/Rarita–Schwinger_equation ). Exploring this further led to supersymmetry. And here's the weird thing ... considering a local supersymmetry freedom leads to gravity.

GR, a theory of the "stage", somehow gave us hints of what physics could even go in this stage.
And now on the other side, looking at the physics, seemed to lead to a requirement on the "stage" itself -> gravity.
Somehow local internal symmetries/freedoms are putting requirements on spacetime symmetries/freedoms! Somehow these are not separate things.

There is something interesting there.
This is being explored.
The math gets difficult, so it takes some brilliant minds to see the meaning amongst all the equations, the forest for the trees if you will. I don't even understand a lot of the current amazing physics, so I'll probably just have to read about it in some popular science rendition as they figure it out. But it's still fun to try to think about.

So currently no one can tell you how the equivalence principle relates or derives from/to other principles. Maybe in time.

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... The equivalence of inertial and gravitational mass is just purely a postulate.
I find it interesting that Galileo concluded that objects with different weights must fall at the same rate in a vacuum, long before they had clocks accurate enough to test this conjecture with any reasonable degree of accuracy. Galilieo reasoned that if for example a 1 kg mass accelerated at 1 m/s/s, a 2 kg mass accelerated at 2 m/s/s and a 3kg mass accelerated at 3 m/s/s, then considering how a 1 kg mass tied to a 2 kg mass would fall would lead to a logical contradiction. The 1 kg mass would slow down the acceleration of the 2 kg mass and the 2 kg mass would speed up the acceleration of the 1 kg mass and so the (1kg+2kg) assembly should accelerate at a rate of somewhere between 1 m/s/s and 2m/s/s which is a contradiction to the initial assumption that a 3 kg mass accelerates at 3 m/s/s. Galileo cocluded that the only logical conclusion is that all masses must fall at the same rate and history has proved him right. To Galileo it was logically absurd that different weights should fall at different rates. The equivalence of gravitational mass and inertial mass is related to Galileo's thought experiment and to Galileo that equivalence is not a conjecture or a postulate, but an inescapable logical conclusion. From this point of view, if some exotic theory about Higg's particles or whatever, predicted that different masses should fall at different rates, then we would have to question the exotic theory before we questioned Galileo's conclusion, because of the very simple "self evident" logic used by Galileo is difficult to defeat. (I think Galileo also described a thought experiment involving bouyancy, that arrives at a similar logical conclusion.)

The equivalence of gravitational mass and inertial mass is related to Galileo's thought experiment and to Galileo that equivalence is not a conjecture or a postulate, but an inescapable logical conclusion.
I find that very interesting. I thought I understood the Galileo thought experiment as it related to the universality of free fall, but I've never heard or read of any relationship between the logic of that experiment and the equivalence of gravitational mass and inertial mass. I would like to know more about this. Does it require a good knowledge of GR?

@kev: Excellent point, but from the standpoint of the scientific method as reflected by a scientific community, no one can accept such a thing on the logic alone. There is a REASON why dropping a feather and a lead weight in a vacuum tube is such an arresting lesson for students. Not merely TELLING them, and having them bask in the logic, but SHOWING them.

If you can't repeat, accept defeat. If you could have gone back in time and demonstrated this "trick" for ancient people, it would have been more impressive than fire. Fire, probably takes generations to regard as anything but magic; "No Air in a tube" is easier. The rest they can see, feel, and experience to some degree. These days, we need the LHC, or LISA to perform the same "Ta Da!", and it naturally takes longer between the logcal clarity of an idea, and even testing it, never mind confirming it.

My question on this topic comes back to what is gravitational mass in GR. In GR it is the energy tensor that causes space-time curvature. This would suggest that Newton's law should be rewritten:

F = G*E1*E2 / c^4*r^2

where E1 and E2 are the total energy of the particle. (For a photon this would be hv, allowing the bending of light. This must be the Newtonian estimate for the bending of light that I have heard is different from GR by a factor of 2).

Now picturing space as one dimentional I can picture energy as a wave on a string. The more energy in the wave the higher the steepness of the slope and the more stretching of the string I would need, more "curvature" would be generated by the wave. I can picture this in two dimentions as a waving parachute thanks to grade school experiences.

Mathematically I can generalize this to three dimentions, but this justification requires a fourth space-like dimention that our three space is bent relative to that we can't otherwise see.

My question on this topic comes back to what is gravitational mass in GR. In GR it is the energy tensor that causes space-time curvature. This would suggest that Newton's law should be rewritten:

F = G*E1*E2 / c^4*r^2

where E1 and E2 are the total energy of the particle. (For a photon this would be hv, allowing the bending of light. This must be the Newtonian estimate for the bending of light that I have heard is different from GR by a factor of 2).

Now picturing space as one dimentional I can picture energy as a wave on a string. The more energy in the wave the higher the steepness of the slope and the more stretching of the string I would need, more "curvature" would be generated by the wave. I can picture this in two dimentions as a waving parachute thanks to grade school experiences.

Mathematically I can generalize this to three dimentions, but this justification requires a fourth space-like dimention that our three space is bent relative to that we can't otherwise see.
Are you suggesting that we live in 4 spatial dimensions + 1 of time?